How do we write ${(\sqrt{7})}^{3}$ $(sqrt7)^3$ in exponential form?

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How do we write ${(\sqrt{7})}^{3}$ $(sqrt7)^3$ in exponential form?

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Answer 1 · 2016-07-20T04:03:52

${(\sqrt{7})}^{3} = 7^{\frac{3}{2}}$ $(sqrt7)^3=7^(3/2)$

Explanation:

To write ${(\sqrt{7})}^{3}$ $(sqrt7)^3$ in exponential form, one needs two identities - $\sqrt[n]{a} = a^{\frac{1}{n}}$ $root(n)a=a^(1/n)$ and ${(a^{m})}^{n} = a^{(m \times n)}$ $(a^m)^n=a^((m×n))$ which is true for all rational $m$ $m$ and $n$ $n$ .

Hence, ${(\sqrt{7})}^{3}$ $(sqrt7)^3$

= ${(7^{\frac{1}{2}})}^{3}$ $(7^(1/2))^3$

= $7^{(\frac{1}{2} \times 3)}$ $7^((1/2×3))$

= $7^{\frac{3}{2}}$ $7^(3/2)$

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How do we write ${(\sqrt{7})}^{3}$ $(sqrt7)^3$ in exponential form?

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