Eighteen 2.5- gallon buckets are needed to fill a cistern of water How many 3-gallon buckets of water will fill the cistern.

15 3-gallon buckets of water will fill the cistern

Step-by-step explanation:

Eighteen 2.5- gallon buckets are needed to fill a cistern of water

This means, 2.5 gallon buckets in 18 places

2.5 gallons × 18 = 1 cistern of water

45 gallons = 1 cistern of water

How many 3-gallon buckets of water will fill the cistern.

Number of 3-gallon bucket in a cistern = Total gallons of bucket in one cistern / 3-gallon buckets

= 45 gallons / 3-gallon buckets

= 15

Number of 3-gallon bucket in a cistern = 15

15 3-gallon buckets of water will fill the cistern

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: