Answer:
[tex](4x^3y^2)^{\frac{3}{10}}=\sqrt[5]{8y^3}\times \sqrt[10]{x^9}[/tex]
Step-by-step explanation:
Given : Expression [tex](4x^3y^2)^{\frac{3}{10}}[/tex]
To find : What is the expression in radical form?
Solution :
The radical form is writing number in square roots, cube roots.
Expression [tex](4x^3y^2)^{\frac{3}{10}}[/tex]
Distribute power into terms,
[tex](4x^3y^2)^{\frac{3}{10}}=(4)^{\frac{3}{10}}\times (x^3)^{\frac{3}{10}}\times (y^2)^{\frac{3}{10}}[/tex]
[tex](4x^3y^2)^{\frac{3}{10}}=(2)^{\frac{3\times 2}{10}}\times (x)^{\frac{3\times 3}{10}}\times (y)^{\frac{3\times 2}{10}}[/tex]
[tex](4x^3y^2)^{\frac{3}{10}}=(2)^{\frac{3}{5}}\times (x)^{\frac{9}{10}}\times (y)^{\frac{3}{5}}[/tex]
[tex](4x^3y^2)^{\frac{3}{10}}=\sqrt[5]{(2)^{3}}\times \sqrt[10]{x^9}\times \sqrt[5]{y^{3}}[/tex]
[tex](4x^3y^2)^{\frac{3}{10}}=\sqrt[5]{8}\times \sqrt[10]{x^9}\times \sqrt[5]{y^{3}}[/tex]
Therefore, The radical form is [tex](4x^3y^2)^{\frac{3}{10}}=\sqrt[5]{8y^3}\times \sqrt[10]{x^9}[/tex]
