Simplify ( sixth root of y)^3*( sixth root of y)^3

${(\sqrt[6]{y})}^{3} \cdot {(\sqrt[6]{y})}^{3}$

Multiply ${(\sqrt[6]{y})}^{3}$ by ${(\sqrt[6]{y})}^{3}$ by adding the exponents.

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

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

Add $3$ and $3$ .

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

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

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

${(y^{\frac{1}{6}})}^{6}$

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

$y^{\frac{1}{6} \cdot 6}$

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

$y^{\frac{6}{6}}$

Cancel the common factor of $6$ .

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Cancel the common factor.

$y^{\frac{6}{6}}$

Divide $1$ by $1$ .

$y^{1}$

Simplify.

$y$

Simplify ( sixth root of y)^3*( sixth root of y)^3

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