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

Answer:

B. $x^{\frac{5}{3}}\cdot y^{\frac{1}{3}}$

Step-by-step 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 $\sqrt[n]{a^m}=a^{\frac{m}{n}$, we can rewrite our given expression as:

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

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

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

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

Therefore, option B is the correct choice.