1 Answer

Nren · Answer 1 · 2020-08-10T03:29:19+0000

Answer:

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
$x^{(2)/(3)}$

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