How do you write $\sqrt[4]{16^{3}}$ $root4(16^3)$ as a fractional exponent?

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How do you write $\sqrt[4]{16^{3}}$ $root4(16^3)$ as a fractional exponent?

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Answer 1 · 2017-05-30T04:39:08

$\sqrt[4]{16^{3}} = 8$ $root(4)(16^3)=8$

Explanation:

As $\sqrt[n]{a} = a^{\frac{1}{n}}$ $root(n)a=a^(1/n)$ and ${(a^{m})}^{\frac{1}{n}} = a^{(m \times \frac{1}{n})} = a^{\frac{m}{n}}$ $(a^m)^(1/n)=a^((mxx1/n))=a^(m/n)$

$\sqrt[4]{16^{3}} = {(16^{3})}^{\frac{1}{4}} = {({(2^{4})}^{3})}^{\frac{1}{4}} = 2^{\frac{4 \times 3}{4}}$ $root(4)(16^3)=(16^3)^(1/4)=((2^4)^3)^(1/4)=2^((4xx3)/4)$

= $2^{\frac{12}{4}} = 2^{3} = 8$ $2^(12/4)=2^3=8$

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How do you write $\sqrt[4]{16^{3}}$ $root4(16^3)$ as a fractional exponent?

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