Simplify ( square root of q^3)/( sixth root of q)

$\frac{\sqrt{q^{3}}}{\sqrt[6]{q}}$

Simplify the numerator.

Factor out $q^{2}$ .

$\frac{\sqrt{q^{2} q}}{\sqrt[6]{q}}$

Pull terms out from under the radical.

$\frac{q \sqrt{q}}{\sqrt[6]{q}}$

Multiply $\frac{q \sqrt{q}}{\sqrt[6]{q}}$ by $\frac{{\sqrt[6]{q}}^{5}}{{\sqrt[6]{q}}^{5}}$ .

$\frac{q \sqrt{q}}{\sqrt[6]{q}} \cdot \frac{{\sqrt[6]{q}}^{5}}{{\sqrt[6]{q}}^{5}}$

Combine and simplify the denominator.

Multiply $\frac{q \sqrt{q}}{\sqrt[6]{q}}$ by $\frac{{\sqrt[6]{q}}^{5}}{{\sqrt[6]{q}}^{5}}$ .

$\frac{q \sqrt{q} {\sqrt[6]{q}}^{5}}{\sqrt[6]{q} {\sqrt[6]{q}}^{5}}$

Raise $\sqrt[6]{q}$ to the power of $1$ .

$\frac{q \sqrt{q} {\sqrt[6]{q}}^{5}}{{\sqrt[6]{q}}^{1} {\sqrt[6]{q}}^{5}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{q \sqrt{q} {\sqrt[6]{q}}^{5}}{{\sqrt[6]{q}}^{1 + 5}}$

Add $1$ and $5$ .

$\frac{q \sqrt{q} {\sqrt[6]{q}}^{5}}{{\sqrt[6]{q}}^{6}}$

Rewrite ${\sqrt[6]{q}}^{6}$ as $q$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[6]{q}$ as $q^{\frac{1}{6}}$ .

$\frac{q \sqrt{q} {\sqrt[6]{q}}^{5}}{{(q^{\frac{1}{6}})}^{6}}$

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

$\frac{q \sqrt{q} {\sqrt[6]{q}}^{5}}{q^{\frac{1}{6} \cdot 6}}$

Combine $\frac{1}{6}$ and $6$ .

$\frac{q \sqrt{q} {\sqrt[6]{q}}^{5}}{q^{\frac{6}{6}}}$

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{q \sqrt{q} {\sqrt[6]{q}}^{5}}{q^{\frac{6}{6}}}$

Rewrite the expression.

$\frac{q \sqrt{q} {\sqrt[6]{q}}^{5}}{q^{1}}$

Simplify.

$\frac{q \sqrt{q} {\sqrt[6]{q}}^{5}}{q}$

Cancel the common factor of $q$ .

Cancel the common factor.

$\frac{q \sqrt{q} {\sqrt[6]{q}}^{5}}{q}$

Divide $\sqrt{q} {\sqrt[6]{q}}^{5}$ by $1$ .

$\sqrt{q} {\sqrt[6]{q}}^{5}$

Rewrite ${\sqrt[6]{q}}^{5}$ as ${(q^{5})}^{\frac{1}{6}}$ .

$\sqrt{q} \sqrt[6]{q^{5}}$

Multiply $\sqrt{q} \sqrt[6]{q^{5}}$ .

Rewrite the expression using the least common index of $6$ .

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

$q^{\frac{1}{2}} \sqrt[6]{q^{5}}$

Rewrite $q^{\frac{1}{2}}$ as $q^{\frac{3}{6}}$ .

$q^{\frac{3}{6}} \sqrt[6]{q^{5}}$

Rewrite $q^{\frac{3}{6}}$ as $\sqrt[6]{q^{3}}$ .

$\sqrt[6]{q^{3}} \sqrt[6]{q^{5}}$

Combine using the product rule for radicals.

$\sqrt[6]{q^{3} q^{5}}$

Multiply $q^{3}$ by $q^{5}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[6]{q^{3 + 5}}$

Add $3$ and $5$ .

$\sqrt[6]{q^{8}}$

Factor out $q^{6}$ .

$\sqrt[6]{q^{6} q^{2}}$

Pull terms out from under the radical.

$q \sqrt[6]{q^{2}}$

Rewrite $\sqrt[6]{q^{2}}$ as $\sqrt[3]{\sqrt{q^{2}}}$ .

$q \sqrt[3]{\sqrt{q^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$q \sqrt[3]{q}$

Simplify ( square root of q^3)/( sixth root of q)

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