Given:
Consider the given expression is
[tex](4x^3y^2)^{\frac{3}{10}}[/tex]
To find:
The radical form of given expression.
Solution:
We have,
[tex](4x^3y^2)^{\frac{3}{10}}=(2^2)^{\frac{3}{10}}(x^3)^{\frac{3}{10}}(y^2)^{\frac{3}{10}}[/tex]
[tex](4x^3y^2)^{\frac{3}{10}}=(2)^{\frac{6}{10}}(x)^{\frac{9}{10}}(y)^{\frac{6}{10}}[/tex]
[tex](4x^3y^2)^{\frac{3}{10}}=(2)^{\frac{3}{5}}(x)^{\frac{9}{10}}(y)^{\frac{3}{5}}[/tex]
[tex](4x^3y^2)^{\frac{3}{10}}=\sqrt[5]{2^3}\sqrt[10]{x^9}\sqrt[5]{y^3}[/tex] [tex][\because x^{\frac{1}{n}}=\sqrt[n]{x}][/tex]
[tex](4x^3y^2)^{\frac{3}{10}}=\sqrt[5]{8y^3}\sqrt[10]{x^9}[/tex] [tex][\because x^{\frac{1}{n}}=\sqrt[n]{x}][/tex]
Therefore, the required radical form is [tex]\sqrt[5]{8y^3}\sqrt[10]{x^9}[/tex].
