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

1 Answer

4 votes

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)}

User Nren
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