Nancy is checking to determine if the expressions x+4+x and 6+2x-2 are equivalent. when x=3 , she correctly finds that both expressions have a value of 10. when x+4+x=14, she correctly evaluates the first expression to find

Expressions are equivalent.

Step-by-step explanation:

Expressions are said to be equivalent if same values are obtained on plugging same number in different expressions

for example

x+4+x at x =3  gives 3+4+3 = 10

6+2x-2 at x=3 gives 6+2(3)-2 = 6+6-2 = 10

therefore given expressions are equivalent.

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:

because they could drop even lower..