Question

What is the expression in radical form? (4x3y2)310

Answer 1

Given:

Consider the given expression is

$(4x^3y^2)^{\frac{3}{10}}$

To find:

The radical form of given expression.

Solution:

We have,

$(4x^3y^2)^{\frac{3}{10}}=(2^2)^{\frac{3}{10}}(x^3)^{\frac{3}{10}}(y^2)^{\frac{3}{10}}$

$(4x^3y^2)^{\frac{3}{10}}=(2)^{\frac{6}{10}}(x)^{\frac{9}{10}}(y)^{\frac{6}{10}}$

$(4x^3y^2)^{\frac{3}{10}}=(2)^{\frac{3}{5}}(x)^{\frac{9}{10}}(y)^{\frac{3}{5}}$

$(4x^3y^2)^{\frac{3}{10}}=\sqrt[5]{2^3}\sqrt[10]{x^9}\sqrt[5]{y^3}$       $[\because x^{\frac{1}{n}}=\sqrt[n]{x}]$

$(4x^3y^2)^{\frac{3}{10}}=\sqrt[5]{8y^3}\sqrt[10]{x^9}$       $[\because x^{\frac{1}{n}}=\sqrt[n]{x}]$

Therefore, the required radical form is $\sqrt[5]{8y^3}\sqrt[10]{x^9}$.