Simplify ( sixth root of y)/( cube root of y)

$\frac{\sqrt[6]{y}}{\sqrt[3]{y}}$

Multiply $\frac{\sqrt[6]{y}}{\sqrt[3]{y}}$ by $\frac{{\sqrt[3]{y}}^{2}}{{\sqrt[3]{y}}^{2}}$ .

$\frac{\sqrt[6]{y}}{\sqrt[3]{y}} \cdot \frac{{\sqrt[3]{y}}^{2}}{{\sqrt[3]{y}}^{2}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt[6]{y}}{\sqrt[3]{y}}$ by $\frac{{\sqrt[3]{y}}^{2}}{{\sqrt[3]{y}}^{2}}$ .

$\frac{\sqrt[6]{y} {\sqrt[3]{y}}^{2}}{\sqrt[3]{y} {\sqrt[3]{y}}^{2}}$

Raise $\sqrt[3]{y}$ to the power of $1$ .

$\frac{\sqrt[6]{y} {\sqrt[3]{y}}^{2}}{{\sqrt[3]{y}}^{1} {\sqrt[3]{y}}^{2}}$

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

$\frac{\sqrt[6]{y} {\sqrt[3]{y}}^{2}}{{\sqrt[3]{y}}^{1 + 2}}$

Add $1$ and $2$ .

$\frac{\sqrt[6]{y} {\sqrt[3]{y}}^{2}}{{\sqrt[3]{y}}^{3}}$

Rewrite ${\sqrt[3]{y}}^{3}$ as $y$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{y}$ as $y^{\frac{1}{3}}$ .

$\frac{\sqrt[6]{y} {\sqrt[3]{y}}^{2}}{{(y^{\frac{1}{3}})}^{3}}$

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

$\frac{\sqrt[6]{y} {\sqrt[3]{y}}^{2}}{y^{\frac{1}{3} \cdot 3}}$

Combine $\frac{1}{3}$ and $3$ .

$\frac{\sqrt[6]{y} {\sqrt[3]{y}}^{2}}{y^{\frac{3}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{\sqrt[6]{y} {\sqrt[3]{y}}^{2}}{y^{\frac{3}{3}}}$

Rewrite the expression.

$\frac{\sqrt[6]{y} {\sqrt[3]{y}}^{2}}{y^{1}}$

Simplify.

$\frac{\sqrt[6]{y} {\sqrt[3]{y}}^{2}}{y}$

Rewrite ${\sqrt[3]{y}}^{2}$ as ${(y^{2})}^{\frac{1}{3}}$ .

$\frac{\sqrt[6]{y} \sqrt[3]{y^{2}}}{y}$

Simplify the numerator.

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

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{y^{2}}$ as $y^{\frac{2}{3}}$ .

$\frac{\sqrt[6]{y} y^{\frac{2}{3}}}{y}$

Rewrite $y^{\frac{2}{3}}$ as $y^{\frac{4}{6}}$ .

$\frac{\sqrt[6]{y} y^{\frac{4}{6}}}{y}$

Rewrite $y^{\frac{4}{6}}$ as $\sqrt[6]{y^{4}}$ .

$\frac{\sqrt[6]{y} \sqrt[6]{y^{4}}}{y}$

Combine using the product rule for radicals.

$\frac{\sqrt[6]{y \cdot y^{4}}}{y}$

Multiply $y$ by $y^{4}$ by adding the exponents.

Multiply $y$ by $y^{4}$ .

Raise $y$ to the power of $1$ .

$\frac{\sqrt[6]{y^{1} y^{4}}}{y}$

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

$\frac{\sqrt[6]{y^{1 + 4}}}{y}$

Add $1$ and $4$ .

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

Simplify ( sixth root of y)/( cube root of y)

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