Question

what is this expression in rational exponent form cuberoot√5xy^2

Answer 1

Answer:

$5^{\frac{1}{3}}x^{\frac{1}{3}}y^{\frac{2}{3}}$.

Step-by-step explanation:

The given expression is

$\sqrt[3]{5xy^2}$

We need to find the expression in rational exponent form.

It can be written as

$(5xy^2)^{\frac{1}{3}}$           $[\because \sqrt[n]{x}=x^{\frac{1}{n}}]$

$=(5)^{\frac{1}{3}}(x)^{\frac{1}{3}}(y^2)^{\frac{1}{3}}$           $[\because (ab)^m=a^mb^m]$

$=5^{\frac{1}{3}}x^{\frac{1}{3}}y^{\frac{2}{3}}$           $[\because (a^m)^n=a^{mn}]$

Therefore, the required expression is  $5^{\frac{1}{3}}x^{\frac{1}{3}}y^{\frac{2}{3}}$.