If a hot tub holds 520 gallons of water, and hose fills the tub at a rate of 6 1/2 gallons every 5 minutes. how long would it take to fill it up

400 minutes

Step-by-step explanation:

To solve this problem we need to divide 520 by the rate and then multiply that answer by 5 minutes.

520/(6 1/2)

520/(13/2) "Changing to improper fraction."

520 * 2/13 "Dividing by a fraction is the same as multiplying by its reciprocal.

1040/13 = 8

5*80=400

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: