Every year on March 14, Asheville holds a pie-eating contest. Each team races to finish a pumpkin pie, a pecan pie, and a blueberry pie as quickly as possible. Last year, Chase and Vicky entered the contest as a team. They each ate the same amount of pie and won! How much pie did each person eat? Write your answer as a proper fraction or mixed number.

Step-by-step explanation:

In order for a participant to win the contest, they need to eat all three pies. Since Chase and Vicky entered the contest as a team of 2 people then each one of them would need to eat 1.5 pies to finish the entire 3 pies. Therefore the fractions would be . Since this would technically be half of the pies then we can simplify the fraction to be (half). Therefore, Chase would eat half of the 3 available pies and Vicky would eat the other half of the 3 available pies to win the contest.

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: