Question

Which expression is equivalent to 3sqt 216x^3y^6z^12

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

Answer 1

The equivalent expression of
`\sqrt[3]{216x^3y^6z^(12)}` is
`6xy^2z^4`

Answer 2

Option 1

`\sqrt[3]{216x^3y^6z^(12)}=6xy^2z^4`

Explanation:

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

To find : Which expression is equivalent to given expression?

Solution :

The given expression is

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

We can write it as,

`=(216x^3y^6z^(12))^{(1)/(3)}`

Applying power rule,
`(x^a)^b=x^(a* b)`

`=(216)^(1)/(3)(x^3)^(1)/(3)(y^6)^(1)/(3)(z^(12))^{(1)/(3)}`

`=(6^3)^(1)/(3)(x^3)^(1)/(3)(y^6)^(1)/(3)(z^(12))^{(1)/(3)}`

`=6xy^2z^4`

Therefore, Option 1 is correct.

`\sqrt[3]{216x^3y^6z^(12)}=6xy^2z^4`