Question

What is the expression in radical form?

(4x3y2)310

Answer 1

Given:

Consider the given expression is

`(4x^3y^2)^{(3)/(10)}`

To find:

The radical form of given expression.

Solution:

We have,

`(4x^3y^2)^{(3)/(10)}=(2^2)^{(3)/(10)}(x^3)^{(3)/(10)}(y^2)^{(3)/(10)}`

`(4x^3y^2)^{(3)/(10)}=(2)^{(6)/(10)}(x)^{(9)/(10)}(y)^{(6)/(10)}`

`(4x^3y^2)^{(3)/(10)}=(2)^{(3)/(5)}(x)^{(9)/(10)}(y)^{(3)/(5)}`

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

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

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