Question

Which expression is equivalent to (x^4/3 x^2/3)^1/3?

Answer 1

The answer is B, x^2/3

Answer 2

Answer : The correct option is, $x^{\frac{2}{3}}$

Step-by-step explanation :

The given expression is :

$(x^{\frac{4}{3}}\times x^{\frac{2}{3}})^{\frac{1}{3}}$

First we have to solve the term present in the bracket.

Identity used : $x^a\times x^b=x^{(a+b)}$

$\Rightarrow (x^{(\frac{4}{3}+\frac{2}{3})})^{\frac{1}{3}}$

By the adding the powers of 'x', we get:

$\Rightarrow (x^{\frac{6}{3}})^{\frac{1}{3}}$

$\Rightarrow (x^{2})^{\frac{1}{3}}$

Now we have to use identity $(x^{a})^b=x^{ab}$, we get :

$\Rightarrow (x)^{(2\times \frac{1}{3})}$

$\Rightarrow (x)^{\frac{2}{3}}$

Therefore, the correct option is, $x^{\frac{2}{3}}$