57 times more material was used to build the Hoover dam than the American falls .
What is Ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.
Given:
Volume of Hover dam = 4 x [tex]10^6[/tex]
Volume of American Falls dam = 7 x [tex]10^4[/tex]
So, the number of times more material used
= Volume of Hover dam / Volume of American Falls dam
= 4 x [tex]10^6[/tex] / 7 x [tex]10^4[/tex]
= 400 x [tex]10^4[/tex] / 7 x [tex]10^4[/tex]
= 57.14
Hence, 57.14 times more material used.
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there are 10 members on a board of directors. if they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible?
There are 720 different slates of candidates possible.
Permutation:
The permutation is a statistical method that determines the number of possible arrangements. In permutation, the order of selection is important and replacements are not allowed.
Permutation can be divided into three different types:
Permutation of n different objects.Repetition, where repetition is allowed.A permutation is when the objects are not distinctThe general formula of Permutations:
[tex]^nP_r=\frac{n!}{(n-r)!}[/tex]
n= total number of members.
r=number of members selected.
Here n=10 and r= 3
Now substitute the values in the above formula:
[tex]^nP_r=\frac{10!}{(10-3)!} \\\\^nP_r=\frac{10!}{7!}\\\\^nP_r= \frac{10*9*8*7!}{7!} \\\\^nP_r=10*9*8\\\\^nP_r=720[/tex]
Therefore, there are 720 different slates of candidates possible.
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Mary, Katherine, and Alex share the bill at a restaurant after a meal. Mary pays for of the bill, Katherine pays for of the bill, and Alex
pays for the rest. What is the ratio of Mary's share to Katherine's share to Alex's share?
The ratio of Mary's share to Katherine's share to Alex's share is 5:4:1, which means Mary pays 5/10 of the bill, Katherine pays 4/10 of the bill, and Alex pays 1/10 of the bill.
To find the ratio, we can write their contribution as a fraction of the total parts and then solve the fractions then they'll have the same denominator.
So, Mary's share is 5/10, Katherine's share is 4/10, and Alex's share is 1/10.
To convert this as a ratio, we write 5:4:1, where each number represents the number of parts each person pays, and the colon separates each person's contribution.
Therefore, the ratio of Mary's share to Katherine's share to Alex's share is 5:4:1
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Here is the graph y = f(x)
(2,-1)
y=f(x)
What are the coordinates of the point
shown after the transformation
f(-2x)?
X
The coordinates of the point shown after the transformation f(-2x) are given as follows:
(-4,-1).
How to apply the transformation?The original coordinates of the the point in this problem are given as follows:
(2,-1).
Hence:
The x-coordinate is of 2.The y-coordinate is of -1.The transformation is given as follows:
f(-2x).
Meaning that the x-coordinate is multiplied by -2, hence the coordinates of the point shown after the transformation f(-2x) are given as follows:
(-4,-1).
(as 2 x -2 = -4).
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1. Divide 180 gallons into three portions with
a ratio of 2:3:4. How much is each part?
Answer:
40:60:80
Step-by-step explanation:
1. add the ratio first 2+3+4 =9, then divide the amount by the total number of parts
2. multiply the quotient by each part (20×2, 20×3 and 20×4)
The two polygons are similar. Find the values of x and y.
Answer:
x = 7.5
y = 166º
Step-by-step explanation:
4 ------ 6
5 ------ x
4x = 30
x = 7.5
116 + 61 + 90 + (y - 73) = 360
y - 73 = 360 - 267
y = 93 + 73
y = 166
Answer:
The other answer shows how to get it but for points just showing his answers are right.
Step-by-step explanation:
find the derivatives of the following functions (2x³-5x²+6x-3)/x² y=sin^-1(x)+cos^-1(x)-Inx y=5^x-6cosec1/2(x)+3/7(cos5x)-2
Answer:
Below
Step-by-step explanation:
1) The derivative of (2x³-5x²+6x-3)/x² is (6x²-10x+6-3x)/x³
2) The derivative of sin^-1(x)+cos^-1(x)-Inx is (1/(√(1-x²))*dx + (-1/(√(1-x²))*dx )- (1/x)*dx
3) The derivative of 5^x - 6cosec1/2(x) + 3/7(cos5x) - 2 is (ln(5) * 5^x) - (6*(-csc(x)cot(x))dx) + (3/7(-5sin(5x))*dx)
suppose that shoe sizes of american women have a bell-shaped distribution with a mean of 8.04 and a standard deviation of 1.53 . using the empirical rule, what percentage of american women have shoe sizes that are less than 11.1 ?
The percentage of American women that have shoe sizes that are at least 11.1 is; 0.0015
Empirical Rule
We are given;
Mean; x' = 8.04
Standard deviation; σ = 1.53
Using the empirical rule, we can have the data either 1, 2, or 3 standard deviations from the mean.
Thus;
At 1 standard deviation from the mean, we have;
8.04 ± 1(1.53)
⇒ (6.52, 8.56)
At 2 standard deviations from the mean, we have;
8.04 ± 2(1.53)
⇒ (5, 11.08)
At 3 standard deviations from the mean, we have;
8.04 ± 3(1.52)
⇒ (3.48, 12.6)
We can see that the one with at least 12,6 is 3 standard deviations from the mean which from the empirical rule is 99.7%
Thus;
percentage of American women have shoe sizes that are at least 12.6 = 100% - 99.7% - 0.15%
P(x ≥ 12.6) = 0.15% = 0.0015
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-cos(x y)sin(y) sin(x y)cos(y)
On the left side of the expression, the first term is cos(x y)sin(y) and the second term is sin(x y)cos( y ).cos(x y)sin(y) sin(x y)cos(y) = cos(x y)sin(y) − sin(x y)cos(y)
We can use the trigonometric identity sin(A)cos(B) - cos(A)sin(B) to simplify the expression.
On the left side of the expression, the first term is cos(x y)sin(y) and the second term is sin(x y)cos( y ).
We can rearrange the terms and apply the identity, which gives us:
On the left side of the expression, the first term is cos(x y)sin(y) and the second term is sin(x y)cos( y ).
cos(x y)sin(y) − sin(x y)cos(y)
the complete question is :
What is the result of cos(x y)sin(y) - sin(x y)cosy?
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The population of a city increases by a rate of 3% a year. In 2000 the population was at 250,000.
A. Write an equation to model the scenario.
B. What was the population in 2010?
Answer: 325000
Step-by-step explanation:
In 2000 the population was 250,000 and it would grow 3 percent a year which is 7500 so that means we add 75000 since 7500 X 10 = 75000 so we add it which gives us 325000 in 2010.
just need this is it thanks very much
The maximum profit that the florist will earn from selling celebration bouquets is $675.
The maximum is given by the vertex of the graph.The florist will break even after 20 one-dollar increases.
Break-even is when profit is zero.The interval of the number of one-dollar increases for which the florist makes a profit from celebration bouquets is [tex](0,20)[/tex].
To make a profit, [tex]P(x)>0[/tex].Which two angles are adjacent?
Answer:
Any angles that share a common vertex and side are adjacent angles.
Solve for x help pleaseee
The value of x in the triangle is 14.4 units.
How to find the side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, let's find the length of x in the right triangle as follows;
Using similar triangle ratios,
x / 18 = 24 / 30
cross multiply
30x = 24 × 18
30x = 432
divide both sides of the equation by 30
x = 432 / 30
x = 14.4
Hence,
x = 14.4 units
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Simplify 2^5x2^2 / 2^7x2^3 leaving your answer in index form
The simplified form of the expression is [tex]2^{-3}[/tex].
What is expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.
Here the given expression is,
=> [tex]\frac{2^5\times 2^2}{2^7 \times 2^3}[/tex]
We know that [tex]a^x\times a^y = a^{x+y}[/tex] then
=> [tex]\frac{2^{5+2}}{2^{7+3}}[/tex]
=> [tex]\frac{2^7}{2^{10}}[/tex]
Now [tex]\frac{a^x}{a^y}=a^{x-y}[/tex] then
=> [tex]2^{7-10}[/tex]
=> [tex]2^{-3}[/tex]
Hence the simplified form of the expression is [tex]2^{-3}[/tex].
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Solve 8x−14≤10. Make sure to write your inequality so that x comes first. (1 point)
(If anyone knows the answer to Lesson 11 inequalities unit test on connections PLS PLS help me!!!)
The solution to the inequality equation given above would be = X ≥ 3
What is inequality equation?An Inequality equation is defined as the type of equation that is used to show the relationship between two variables that are not equal using the following symbols such as < or >.
The equation given are as follows:
= 8x−14≤10
Bring the like terms together;
= 8x ≤ 10+14
= 8x ≤ 24
= X ≥ 24/8
= X ≥ 3
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The solution to the inequality equation is expressed as; x ≤ 3
What is inequality equation?Equations and inequalities are considered to be both mathematical sentences that are formed by relating two expressions to each other. In an equation, the two expressions are considered as equal which is shown by the symbol =. Meanwhile in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
The equation we are to solve is; 8x − 14 ≤ 10
Add 14 to both sides to get;
8x ≤ 24
Divide both sides by 8 to get;
x ≤ 3
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the sum of lisa's age and myra's age is 40. in to years, lisa will be 3 times as old as myra. how old is each person now?
The age of Lisa and Myra now is 35 years old and 5 years old, respectively.
To determine how old each person now, use algebraic expression and equation.
Let x = current age of Lisa
y = current age of Myra
If the sum of Lisa's age and Myra's age is 40, then we can express it as:
x + y = 40
x = 40 - y
If in 10 years, Lisa will be 3 times as old as Myra, then we can express it as:
x + 10 = 3(y + 10)
x + 10 = 3y + 30
x - 3y = 20
Substitute the equation for x into the 2nd equation and solve for y.
x - 3y = 20
(40 - y) - 3y = 20
40 - 4y = 20
4y = 20
y = 5
Substitute the value of y into the equation for x and solve.
x = 40 - y
x = 40 - 5
x = 35
Therefore, Lisa is 35 years old while Myra is 5 years old.
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Two families visited an amusement park. the first family bought 2 hot dogs and 3 bottles of waters, which totaled $18. the second family bought 4 hot dogs and 2 bottles of waters, which totaled $28. how much did one hot dog cost? a. $2 b. $4c. $5 d. $6
Answer:
d. $6
Step-by-step explanation:
Need help asappppp thank youuuuu
30 * x⁵y⁸ will be the volume of the given rectangular prism.
What is volume?Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m3), a derived unit, is the SI unit of volume. Volume is another word for capacity.
Given a rectangular prism whose sides are mentioned in the problem.
From the general formula of the Volume of Cuboid:
Volume of cuboid = length *width*height
In our case,
Length = 3x²y²
Width = 5x²y⁴
Height = 2xy²
Thus,
volume of rectangular prism = 3x²y²* 5x²y⁴ * 2xy²
volume of rectangular prism = 30 * x⁵y⁸
therefore, the volume of the given rectangular prism will be 30 * x⁵y⁸.
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Find the length of BC
Our legs range in length from 15 to 36. (A & B). A hypotenuse is 39.
What is Pythagorean Theorem?Any right triangle has a square whose side is the hypotenuse, which is the side across from the right angle, and whose area is equal to the sum of the squares' areas whose sides are the two legs (the two sides that meet at a right angle). The square on the hypotenuse is equal to the sum of the squares on the other two sides for all right-angled triangles, according to Pythagoras' theorem. The longest side is called the hypotenuse, and it is always perpendicular to the right angle. A right angle is formed in this triangle using the formula a 2 = b 2 + c 2.We must apply Pythagorean Theorem in order to solve for this.
In order to find the hypotenuse (C), or the side that is opposite the 90-degree angle, we add the squares of the legs (A & B). This is known as the Pythagorean Theorem.
A² + B² = C² is the Pythagorean Theorem's formula.
We have two different leg lengths: 15 and 36. (A & B).
Square 15 and 36.
15² = 225
36² = 1,296
Let's add the side lengths now that we have them.
225 + 1,296 = 1,521.
We now need to square root our sum in order to find C.
39 is the square root of 1,521.
39 is your hypotenuse.
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sam is going to assemble a computer by himself. he has choice of chips from two bands, a hard dive from four, memory from three and an accessory bundle from five local stores. how many different ways can sam order the parts?
The total number of different combinations Sam can make is 120.
Computer Assembly Options CalculationThe number of different ways that Sam can order the parts is given by the product of the number of choices he has for each part:
Chips: 2 options
Hard Drive: 4 options
Memory: 3 options
Accessory Bundle: 5 options
Therefore, the total number of different combinations Sam can make is 2 x 4 x 3 x 5 = 120.
This is about a person named Sam who is assembling a computer and has a choice of parts from different brands and stores. The problem is to calculate the number of different combinations of parts he can choose from. The solution involves finding the number of options he has for each part (chips, hard drive, memory, and accessory bundle) and then multiplying these numbers to get the total number of combinations.
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Deepak used 32% of his salary to pay the house rent which amounted to 16,000. What is his total salary?
Answer:
50,000
Step-by-step explanation:
The diameter of a hat is 6.8 inches. What is the distance around the hat using π = 3.14? Round to the hundredths place.
2.17 inches
10.68 inches
21.35 inches
36.29 inches
Answer:
Step-by-step explanation:
c is the correct answer
Answer: c
Step-by-step explanation:
FIND AREA PLS HELP ASAP
The area of the rhombus is 54 sq. units
Area of the trapizium is 115 sq. units.
What is a Rhombus and Trapizium ?A quadrilateral called a rhombus has four equal-length sides. The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths.
A parallelogram's general characteristics are as follows:
Angles on the opposite sides are congruent or equal.The opposing sides are parallel and equal in size.Diagonals cut each other in half.Any two parallel or following angles add up to 180 degrees.In American and Canadian English, a quadrilateral having at least one set of parallel sides is referred to as a trapezoid. It is referred to as a trapezium in British and other varieties of English. In Euclidean geometry, a trapezoid is a convex quadrilateral by definition. The bases of the trapezoid are the parallel sides.
The area of a rhombus = ½ x (product of the lengths of the diagonals)
= ½ *18*6 = 54 sq. units
Area of the trapizium = ½ x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sides
=½ *(17 + 29) * 5 = 115 sq. units.
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If triangle ABC is rotated 90 degrees clockwise about the origin followed by dilation by a factor of 2 about the origin, what will be the resulting coordinates of the vertices of the transformed triangle A' B'C'?
For a ΔABC when rotated 90° clockwise and dilated with a factor of 2 the new vertices becomes option C: A'(0,4), B'(6,-4) and C'(-2,-2).
What is dilation?
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial shape should be stretched or contracted during a dilatation.
The vertices of triangle ABC are - A(-2,0), B(2,3) and C(1,-1).
When an object is rotated at an angle of 90° clockwise the formula for the vertices becomes (x,y) → (y,-x)
So, the new vertices are -
A(-2,0) → [(0),-(-2)] → a(0,2)
B(2,3) → [(3),-(2)] → b(3,-2)
C(1,-1) → [(-1),-(1)] → c(-1,-1)
When an object is dilated by a factor of 2 the formula for the vertices becomes (x,y) → (2x,2y)
So, the new vertices are -
a(0,2) → [2(0),2(2)] → A'(0,4)
b(3,-2) → [2(3),2(-2)] → B'(6,-4)
c(-1,-1) → [2(-1),2(-1)] → C'(-2,-2)
Therefore, the new vertices are A'(0,4), B'(6,-4) and C'(-2,-2).
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At a pizza shop, 6 slices of pizza and 2 drinks cost the same as 5 slices of pizza and 5 drinks. Each slice of pizza costs $4.50. Find the cost in dollars of each drink.
Answer:
Each drink costs $1.50
Step-by-step explanation:
Let d = the cost of a drink
6(4.50) + 2d = 5(4.5) + 5d Distribute the 6 and 5
27 + 2d = 22.50 + 5d Subtract 2d from both sides
27 + 2d - 2d = 22.50 + 5d - 2d
27 = 22.50 + 3d Subtract 22.50 from both sides
4.5 = 3d Divide both sides by 3
1.50 = d
PLS DO NUMBER NUMBER 6 WILL GIVE 75 pts
Answer:
Step-by-step explanation:
THE CONSTANT RATE WILL BE 2.5 so that would =75%
condense the equation
2log9= log3 - logx
Answer:
[tex]x=\frac{1}{27}[/tex]
Step-by-step explanation:
Solve for x.
We need to use the quotient property of logarithms.
Quotient Property of Logarithms: [tex]\log _{b} (x)-\log _{b} (y)=\log _{b} (\frac{x}{y} )[/tex]
Apply the property to our equation.
[tex]\log(\frac{3}{x})=2\log(9)[/tex]
Simplify the right side by moving the 2 inside the logarithm.
[tex]\log(\frac{3}{x})=\log(9^2)[/tex]
For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.
[tex]\frac{3}{x}=9^2[/tex]
Evaluate [tex]9^2[/tex].
[tex]\frac{3}{x}=81[/tex]
Multiply both sides of the equation by x.
[tex]\frac{3}{x}x=81x[/tex]
Cancel the common factor of x on the left side.
[tex]3=81x[/tex]
Divide both sides by 81.
[tex]\frac{3}{81} =\frac{81x}{81}[/tex]
[tex]\frac{3}{81} =x[/tex]
Simplify the fraction.
[tex]x=\frac{1}{27}[/tex]
what is the sum (two-fifths x startfraction 5 over 8 endfraction) (one-fifth x minus one-fourth)? three-fifths x startfraction 1 over 8 endfraction three-fifths x startfraction 3 over 8 endfraction three-fifths x startfraction 5 over 8 endfraction three-fifths x startfraction 7 over 8 endfraction
The sum of the expressions 2x/5 + 5/8 + x/5 - 1/4 is option b) 3x/8 + 3/8
Here we have 2x/5 + 5/8 + x/5 - 1/4
Now since we have constants as well as variables here, to add these up, we will add the constants and variables separately.
The constants are the ones with just numbers, while the variables are those terms that have the term x with them.
Hence adding up the constants will give us
5/8 - 1/4
The LCM of denominators 8, and 4 is 8
Hence, we get
5/8 - 2/8
= 3/8
Now adding the variable gives us
2x/5 + x/5
= 3x/5
Hence the sum is
3x/5 + 3/8
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Complete Question
2x/5 + 5/8 + x/5 - 1/4
a) 3x/5 + 1/8
b) 3x/5 + 3/8
c) 3x/5 + 5/8
d) 3x/5 + 7/8
It is not equal to any of the options listed: three-fifths x 1/8, three-fifths x 3/8, three-fifths x 5/8, or three-fifths x 7/8.
The expression
(2/5 * 5/8) + (1/5 * x - 1/4)
can be simplified as follows:
2/5 * 5/8 = 1/8
1/5 * x - 1/4 = (1/5 - 1/4) x = -3/20 x
So the expression becomes
1/8 + (-3/20 x) = (1/8 - 3/20 x).
This is not equal to any of the options listed: three-fifths x 1/8, three-fifths x 3/8, three-fifths x 5/8, or three-fifths x 7/8.
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HELP MEEEE!!!
i really need helppp
The value of a and b are 1 and 6 respectively.
The equation of the line is y = 1 / 3 x + 1.
How to find the equation of a line?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slope of the lineb = y-interceptTherefore, let's find the value of a and b using the line.
Hence, using (3, 2) and (12, 5)
slope = 5 - 2 / 12 - 3
slope = 3 / 9
slope = 1 /3
Therefore, let's find the y-intercept using (3, 2)
y = 1 / 3 x + b
2 = 1 /3 (3) + b
2 - 1 = b
b = 1
Therefore, the equation is y = 1 / 3 x + 1.
Let's find a and b
a is the y-intercept. Therefore, a = 1
using (b, 3)
y = 1 / 3 x + 1
3 = 1 / 3 (b) + 1
3 - 1 = b / 3
b = 2 × 3
b = 6
Therefore,
a = 1 and b = 6
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question 6: orthogonal matrices let r be an n×northogonal matrix. 1. what values can the determinant of r take? 2. what values can the real eigenvalues take?
An orthogonal matrix has determinant and real eigenvalues of either 1 or -1, depending on the orientation and reflection properties of the matrix.
An orthogonal matrix is a special type of square matrix where the transpose of the matrix is equal to its inverse.
The determinant of an orthogonal matrix is either 1 or -1. This is because the determinant of a matrix represents the scaling factor of the matrix and an orthogonal matrix can only scale the space by a factor of 1 or -1.
The determinant of 1 indicates that the matrix preserves orientation, while a determinant of -1 indicates that the matrix reflects the space.
The real eigenvalues of an orthogonal matrix are either 1 or -1. This is because an orthogonal matrix preserves the magnitude of vectors, and therefore, the eigenvalues must be either 1 or -1.
The number of eigenvalues equal to 1 is equal to the number of dimensions preserved by the matrix, and the number of eigenvalues equal to -1 is equal to the number of dimensions reflected by the matrix.
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Gina Wilson all things algebra Unit 6 Homework 5
The simplified monomials are:
-2a³b²xy(7 - 2x)3a⁷-x¹⁰k⁴15x⁷-12x⁵y⁵10b⁸/a³16y⁸a⁸b¹⁰c¹⁵d³/216c³1/64a⁷-576x¹¹y⁸64b¹⁵/a³c⁹3/d²3a⁴/2b-4x²yz³8y⁵/581x⁸/y¹²-5a³bLet's simplify each monomials we have.
3a³b² - 5a³b² = -2a³b² --> both exponents are already equal
5xy - 2x²y + 2xy = 7xy - 2x²y
= xy (7 - 2x)
-6w : -2w = 3
a⁴ . a³ = a⁽⁴⁺³⁾
= a⁷
(-x⁵)² = - x ⁽⁵ˣ²⁾
= - x¹⁰
k⁹ / k⁵ = k⁽⁹⁻⁵⁾
= k⁴
-5x³ . (-3x⁴) = 15x⁷
(-2x²y)² . (-3xy³) = (4x⁴y²) . (-3xy³)
= -12x⁵y⁵
2a⁻⁵b⁶ . 5a²b² = 10 a⁻³b⁸
= 10b⁸ / a³
(-4y⁴)² = 16y⁸
(a²bc³)⁴ . (b²c)³ = (a⁸b⁴c¹²) . (b⁶c³)
= a⁸b¹⁰c¹⁵
(6cd⁻¹)⁻³ = 1 / (6cd⁻¹)³
= (d/6c)³
= d³ / 216c³
(4a)⁻³ . a⁻⁴ = 1/(4a)³ . (1/a⁴)
= 1/64a³ . 1/a⁴
= 1/64a⁷
(3xy)² . (-4x³y²)³ = (9x²y²) . (-64x⁹y⁶)
= -576x¹¹y⁸
(4a⁻¹b⁵c⁻³)³ = (4b⁵ / ac³)³
= 64b¹⁵ / a³c⁹
9d⁸/3d¹⁰ = 3/d²
6a⁵b² / 4ab³ = 3a⁴/ 2b
32x³y²z⁵ / -8xyz² = -4x²yz³
(2y⁵)⁴ / 10y¹⁵ = 16y²⁰ / 10y¹⁵
= 8y⁵ / 5
(3x⁵y³ / x³y⁶)⁴ = (3x²/y³)⁴
= 81x⁸ / y¹²
(-6a⁵b)² - 8a³b = 36a¹⁰b² - 8a³b
12a⁷b 12a⁷b
= 3a⁵b - 8a⁵b
= -5a⁵b
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