The math club is baking pies for a bake sale the fruit pie recipe calls for twice as many peaches as nectarines if it takes a total of 168 pieces of fruit for all the pies, how many nectarines are needed?

112 nectarines are needed.

Step-by-step explanation:

The math club is baking pies for a bake sale and they would require a number of peaches and nectarines

Let x represent the number of peaches.

Let y represent the number of peaches.

The fruit pie recipe calls for twice as many peaches as nectarines. This is expressed as

y = 2x

if it takes a total of 168 pieces of fruit for all the pies, it means that

x + y = 168 - - -- - - - - - 1

Substituting y = 2x into equation 1, it becomes

x + 2x = 168

3x = 168

x = 168/3 = 56

y = 2x

y = 2×56 = 112

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: