Question

Which is equivalent

Answer 1

Answer: Second option

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

Explanation:

By definition we know that:

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

In this case we have the following expression

`\sqrt[3]{x^5y}`

Using the property mentioned above we can write an equivalent expression for
`\sqrt[3]{x^5y}`

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

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

Therefore the correct option is the second option

Answer 2

`x^(5)/(3) y^(1)/(3)`

Explanation:

This question is on rules of rational exponential

where the exponential is a fraction, you can re-write it using radicals where the denominator of the fraction becomes the index of the radical;

General expression

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

Thus
`\sqrt[3]{x} =x^(1)/(3)`

Applying the same in the question

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

=
`x^(5)/(3) y^(1)/(3)`