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Find k if \(\large \sqrt[3]{x\sqrt{x}} = x^k \)

 Jul 1, 2020
 #1
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\(\sqrt[3]{x\sqrt{x}}=x^k\)

\(\sqrt[3]{x\cdot x^\frac{1}{2}}=x^k\)

\(\sqrt[3]{x^\frac{3}{2}}=x^k\)

\(x^{\frac{3}{2}\cdot\frac{1}{3}}=x^k\)

\(x^\frac{1}{2}=x^k\)

\(\boxed{k=\frac{1}{2}}\)

\(\)

.
 Jul 1, 2020

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