Question

Which is equivalent to RootIndex 5 StartRoot 1,215 EndRoot Superscript x?

243x
1,215 Superscript one-fifth x
1,215 Superscript StartFraction 1 Over 5 x EndFraction
243 Superscript StartFraction 1 Over x EndFraction

Answer 1

b. 1,215 Superscript one-fifth x

Explanation:

Answer 2

1,215 Superscript one-fifth x

Explanation:

Given:

The expression to simplify is given as:

`(\sqrt[5]{1215})^x`

We know that,

`\sqrt[n]{a} = a^{(1)/(n)}`

Here,
`n=5, a=1215`

So,
`\sqrt[5]{1215} = 1215^{(1)/(5)}`

So, the above expression becomes:

`(\sqrt[5]{1215})^x = (1215^{(1)/(5)})^x`

Now, using the law of indices
`(a^m)^n=a^((m* n))`

Here,
`a=1215,m=(1)/(5),n=x`

So, the expression is finally simplified to;

`=(1215)^{({(1)/(5)}* x)}\\\\=(1215)^{(1)/(5)x}`

Therefore, the second option is the correct one.

`(\sqrt[5]{1215})^x` = 1,215 Superscript one-fifth x