One maid can clean the house in 2 hours. Another maid can do the job in 8 hours. How long will it take them to do the job working together?
A 16/6 hr
B 8/5 hr
C 1/10 hr
D 1/16 hr

Option B, 8/5 hr

Step-by-step explanation:

1/2 + 1/8

1*4 / 2*4 + 1/8

4/8 + 1/8

5/8 = 1/t

5t / 5 = 8 / 5

t = 8/5

 Option B, 8/5 hr

B 8/5 hr

Step-by-step explanation:

One maid can clean the house in 2 hours. This means that the rate at which she cleans the house per hour is 1/2

Another maid can do the job in 8 hours. This means that the rate at which the other maid cleans the house per hour is 1/8

If they work together, they would work simultaneously and their individual rates are additive. This means that their combined working rate would be

1/2 + 1/8 = 5/8

Assuming it takes t hours for both of them to clean the room working together, the working rate per hour would be 1/t. Therefore,

5/8 = 1/t

t = 8/5 hour

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: