Question

Which expression is equivalent to ^3 square root 216x^3 y^6 z^12 ?

6xy^2 z^4
18xy^3 z^6
36xy^2 z^4
72xy^3 z^6

Answer 1

Alternative 1 ) 6xy^2z^4
hope it helps

Answer 2

Option A.

Explanation:

The given expression is

`\sqrt[3]{216x^3y^6z^(12)}`

We need to find the simplified form of the given expression.

It can be rewritten as

`\sqrt[3]{6^3x^3y^6z^(12)}`

Using the properties of exponents, we get

`(6^3x^3y^6z^(12))^{(1)/(3)}`
`[\because \sqrt[n]{x}=x^{(1)/(n)}]`

`(6^3)^{(1)/(3)}(x^3)^{(1)/(3)}(y^6)^{(1)/(3)}(z^(12))^{(1)/(3)}`
`[\because (ab)^x=a^xb^x]`

`6^{(3)/(3)}x^{(3)/(3)}y^{(6)/(3)}z^{(12)/(3)}`
`[\because (x^m)^n=x^(mn)]`

`6^(1)x^(1)y^(2)z^(4)`

`6xy^(2)z^(4)`

Hence, the correct option is A.