A cube with a volume of 75 cmis dilated by a factor of 5.
What is the volume of the dilated cube?

The volume of the dilated cube is

Explanation:

The volume of the cube is

It is given that the cube is dilated by a factor of 5.

We need to determine the volume of the dilated cube.

Since, we know that the dilation is a transformation that changes the size of the image but not the shape.

Since, it is given that the volume of the cube is dilated by a factor of 5, the length of the image will be 5 times greater, the width of the image will be 5 times greater and the height of the image will be times greater than the original image.

Thus, the volume of the dilated cube is given by,

Thus, the volume of the dilated cube is

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: