How do you write this expression in radical form ${(x^{2})}^{\frac{4}{3}}$ $(x^2)^(4/3)$ ?

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How do you write this expression in radical form ${(x^{2})}^{\frac{4}{3}}$ $(x^2)^(4/3)$ ?

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Answer 1 · 2016-07-30T07:49:00

${(x^{2})}^{\frac{4}{3}} = {\sqrt[3]{x}}^{8}$ $(x^2)^(4/3)=root(3)x^8$

Explanation:

As ${(a^{m})}^{n} = a^{m n}$ $(a^m)^n=a^(mn)$ , ${(x^{2})}^{\frac{4}{3}} = x^{2 \times \frac{4}{3}} = x^{\frac{8}{3}}$ $(x^2)^(4/3)=x^(2xx4/3)=x^(8/3)$

Now, in radical form $a^{\frac{1}{p}} = \sqrt[p]{a}$ $a^(1/p)=root(p)a$

Hence $x^{\frac{8}{3}} = {(x^{8})}^{\frac{1}{3}} = {\sqrt[3]{x}}^{8}$ $x^(8/3)=(x^8)^(1/3)=root(3)x^8$

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How do you write this expression in radical form ${(x^{2})}^{\frac{4}{3}}$ $(x^2)^(4/3)$ ?

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