Question

Which is equivalent

Answer 1

Answer:

$x^\frac{5}{3} y^\frac{1}{3}$

Step-by-step 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

$a^\frac{1}{n} =\sqrt[n]{a}$

Thus    $\sqrt[3]{x} =x^\frac{1}{3}$

 

Applying the same in the question

$\sqrt[3]{x^5y} =x^\frac{5}{3} y^\frac{1}{3}$

=$x^\frac{5}{3} y^\frac{1}{3}$

Answer 2

Answer: Second option

$(x^5y)^{\frac{1}{3}} = x^{\frac{5}{3}}y^{\frac{1}{3}}$

Step-by-step explanation:

By definition we know that:

$a ^{\frac{m}{n}} = \sqrt[n]{a^m}$

In this case we have the following expression

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

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

$\sqrt[3]{x^5y} = (x^5y)^{\frac{1}{3}}$

$(x^5y)^{\frac{1}{3}} = x^{\frac{5}{3}}y^{\frac{1}{3}}$

Therefore the correct option is the second option