The committee is planning a party and 180 guests are expected. each bottle of juice contains enough for 16 servings. how many bottles of juice will be needed to give each person 1 serving? 11121642880

The total number of guests expected at the party = 180 guests

Since each guest is given 1 serving, the total number of servings of juice required = 180 servings

Each bottle of juice satisfies 16 servings

Therefore, number of bottles of juice required = Total number of servings at the party/ number of servings per bottle of juice

Therefore, number of bottles of juice required = 180/16 = 11.25 bottles of juice

Since we cannot have a fractional bottle of juice, we round 11.25 as 12 bottles of juice

Number of bottles of juice needed = 12 bottles

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: