Question

Please help quickly!!! 

Which equation shows the correct use of the Power of Products Property?
A. (2x^5y^2)^3=6x^5y^2
B. (2x^5y^2)^3=6x^15y^6
C. (2x^5y^2)^3=8x^8y^5
D. (2x^5y^2)^3=8x^15y^6

Answer 1

`(2x^5y^2)^3=2^3 * (x^5)^3 * (y^2)^3=8 * x^(5 * 3) * y^(2 * 3)=8x^(15)y^6`

The answer is D.

Answer 2

Option D is correct.

`(2x^5y^2)^3= 8x^(15)y^6`

Explanation:

Power of product property:

• 
  `(x^m)^n = x^(mn)`

• 
  `(ax)^m = a^m \cdot x^m`

Let the equation:
`(2x^5y^2)^3`

Using power of products Property on given equation:

`(2x^5y^2)^3` =
`2^3 \cdot (x^5)^3 \cdot (y^2)^3 = 8 \cdot x^(15) \cdot y^6 = 8x^(15)y^6`

Therefore, the only option D of an equation which shows the correct use of power of Products property is,
`(2x^5y^2)^3= 8x^(15)y^6`