An auto service center that specializes in oil changes has two service bays that serve, on average, a total of 24 cars per eight-hour business day. On average, each bay can finish one oil change in 30 minutes.

What is the design capacity? 30 min per oil change per bay (8 hr day x 2 (30 min each) =16 x 2 bays =?)

Step-by-step explanation:

Given

Number of service bays

Time taken by each bay to finish one oil change

Working capacity hours per day

Thus, in hours the total number of times one bay has changed the oil is equal to

If one service bay's capacity is equal to , capacity of two service bays is equal to

Thus, the design capacity 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: