Question

Which expression is equivalent to 3sqrtx^5y?

A)x^(5/3)y
B)x^(5/3)y^(1/3)
C)x^3/5y
D)x^3/5y^3

Answer 1

∛x^5y = x^5/3 y^1/3

answer is B.
x^5/3 y^1/3

Answer 2

B.
`x^{(5)/(3)}\cdot y^{(1)/(3)}`

Explanation:

We have been given a radical expression
`\sqrt[3]{x^5y}`. We are asked to find the equivalent expression for our given expression.

We can rewrite our given expression as:

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

Using exponent property for radicals
`\sqrt[n]{a^m}=a^{(m)/(n)`, we can rewrite our given expression as:

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

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

Upon substituting these values in expression
`\sqrt[3]{x^5}\cdot \sqrt[3]{y}`, we will get,

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

Therefore, option B is the correct choice.