Question

Which expression is equivalent to 3(sqrt)125x^6y^15z^3?

A. 5x^3y^3z
B. 5x^2y^5z
C. 25x^2y^3z
D. 25x^2y^5z

Answer 1

B. would be the correct choice here

Answer 2

B.
`5x^2 y^5 z`

Explanation:

Given expression is,

`\sqrt[3]{125x^6y^(15)15z^3}`

`=\sqrt[3]{(5^3)(x^2)^3(y^5)^3(z)^3}` (
`(a^(mn)=(a^m)^n` )

`=\sqrt[3]{(5x^2 y^5 z)^3}` (
`a^m.b^m=(ab)^m` )

`=((5x^2 y^5 z)^3)^{(1)/(3)}` (
`\sqrt[m]{a}=a^{(1)/(m)}` )

`=(5x^2 y^5 z)^{3* {(1)/(3)}`

`=(5x^2 y^5 z)^1`

`=5x^2 y^5 z`

Hence, option B is correct.