An office and apartment building is made up of modules. Each module is a rectangular

prism. The building has 130 modules, and is 13 stories high.

If all of the modules were divided evenly among the number of stories, how many modules

would be on each floor?

How many different rectangular prisms could be made from that number?

If all of the modules were divided evenly there would be 10

modules on each floor.

different rectangular prisms could be made from the number of modules on each

Three

floor:

I

x 1 x 1 and 2 x

* 1.

(a)10 modules per floor

(b)Two different rectangular prism

Step-by-step explanation:

Part A

Number of modules=130

Number of stories=13

Since all of the modules were divided evenly among the number of stories:

Number of module per floor =130÷13=10 modules per floor

There would be 10 modules on each floor.

Part B

Next, we determine how many different rectangular prisms could be made from the number 10 derived above.

Step 1: List the factors of 10

Factors of 10 are: 1,2,5 and 10

Step 2:

Form a product of three terms which equals 10 using the factors derived above. We have two possible combinations:

Therefore, two different rectangular prisms could be made from the number of modules on each floor.

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: