Stephanie puts 30 cubes in a box. each cube is 1/2 an inch on each side. The box holds 2 layers of 15 cubes. what is the volume of the box

3.75 cubic inches

Step-by-step explanation:

Volume = length x breadth x height

since the box holds 2 layers of 15 cubes

length contains 5 cubes= 5x1/2 inches=2.5 inches

breadth contains 3 cubes=3x1/2inches=1.5 inches

height contains 2 cubes=2x1/2inches=1.0 inches

Volume=2.5x1.5x1.0=3.75 cubic inches

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:

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square