Question

Which expression is equivalent to (x4/3 x2/3)^1/3?

Answer 1

Thus,
`(x^{(4)/(3)}x^{(2)/(3)})^{(1)/(3)}` is equivalent to
`x^{(2)/(3)}`

Explanation:

Consider the given expression

`(x^{(4)/(3)}x^{(2)/(3)})^{(1)/(3)}`

Using property of exponents
`a^ma^n=a^(m+n)`

Here, a = x ,
`m=(4)/(3) , n=(2)/(3)`

`(x^{(4)/(3)}x^{(2)/(3)})^{(1)/(3)}=(x^{(4)/(3)+(2)/(3)})^(1)/(3)`

Solving further,

`\Rightarrow (x^{(4+2)/(3)})^(1)/(3)`

`\Rightarrow (x^{(6)/(3)})^(1)/(3)`

`\Rightarrow (x^2)^(1)/(3)`

Again using property of exponents
`(a^m)^n=a^(mn)`

We get ,
`(x^2)^(1)/(3)=x^{(2)/(3)}`

Thus,
`(x^{(4)/(3)}x^{(2)/(3)})^{(1)/(3)}` is equivalent to
`x^{(2)/(3)}`