Which equation applies the associative property of multiplication? a: (−4/11−2/3)−3/4=−4/11−(2/3−3/4) b: −12/5⋅(7/12⋅1/9)⋅8/5=(−12/5⋅7/12)⋅( 1/9⋅8/5) c: 1/2⋅(5/8+3/6)=(1/2⋅5/8)+(1/2⋅3/6) d: 4/9⋅(−3/8)⋅9/4=4/9⋅9/4⋅(−3/8)

The correct answer D) 4/9⋅(−3/8)⋅9/4=4/9⋅9/4⋅(−3/8)

Step-by-step explanation:

This property states that no matter which way we group things when multiplying, they will still create the same outcome. Since all of the symbols are multiplication, the answer is the same even though the order of the numbers is different.

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: