Write in Exponential Form ( fifth root of x)^(5/6)* square root of x

${(\sqrt[5]{x})}^{\frac{5}{6}} \cdot \sqrt{x}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{x}$ as $x^{\frac{1}{5}}$ .

${(x^{\frac{1}{5}})}^{\frac{5}{6}} \cdot \sqrt{x}$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

${(x^{\frac{1}{5}})}^{\frac{5}{6}} \cdot x^{\frac{1}{2}}$

Step 3

Multiply the exponents in ${(x^{\frac{1}{5}})}^{\frac{5}{6}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{1}{5} \cdot \frac{5}{6}} \cdot x^{\frac{1}{2}}$

Cancel the common factor of $5$ .

Cancel the common factor.

$x^{\frac{1}{5} \cdot \frac{5}{6}} \cdot x^{\frac{1}{2}}$

Rewrite the expression.

$x^{\frac{1}{6}} \cdot x^{\frac{1}{2}}$