Simplify 20 root of (y^-8)/(y^-3)

$\sqrt[20]{\frac{y^{- 8}}{y^{- 3}}}$

Step 1

Reduce the expression $\frac{y^{- 8}}{y^{- 3}}$ by cancelling the common factors.

Multiply by $1$ .

$\sqrt[20]{\frac{y^{- 8} \cdot 1}{y^{- 3}}}$

Factor $y^{- 8}$ out of $y^{- 3}$ .

$\sqrt[20]{\frac{y^{- 8} \cdot 1}{y^{- 8} y^{5}}}$

Cancel the common factor.

$\sqrt[20]{\frac{y^{- 8} \cdot 1}{y^{- 8} y^{5}}}$

Rewrite the expression.

$\sqrt[20]{\frac{1}{y^{5}}}$

Step 2

Rewrite $1$ as $1^{5}$ .

$\sqrt[20]{\frac{1^{5}}{y^{5}}}$

Step 3

Rewrite $\frac{1^{5}}{y^{5}}$ as ${(\frac{1}{y})}^{5}$ .

$\sqrt[20]{{(\frac{1}{y})}^{5}}$

Step 4

Rewrite $\sqrt[20]{{(\frac{1}{y})}^{5}}$ as $\sqrt[4]{\sqrt[5]{{(\frac{1}{y})}^{5}}}$ .

$\sqrt[4]{\sqrt[5]{{(\frac{1}{y})}^{5}}}$

Step 5

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

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

Step 6

Rewrite $\sqrt[4]{\frac{1}{y}}$ as $\frac{\sqrt[4]{1}}{\sqrt[4]{y}}$ .

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

Step 7

Any root of $1$ is $1$ .

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

Step 8

Multiply $\frac{1}{\sqrt[4]{y}}$ by $\frac{{\sqrt[4]{y}}^{3}}{{\sqrt[4]{y}}^{3}}$ .

$\frac{1}{\sqrt[4]{y}} \cdot \frac{{\sqrt[4]{y}}^{3}}{{\sqrt[4]{y}}^{3}}$

Step 9

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt[4]{y}}$ by $\frac{{\sqrt[4]{y}}^{3}}{{\sqrt[4]{y}}^{3}}$ .

$\frac{{\sqrt[4]{y}}^{3}}{\sqrt[4]{y} {\sqrt[4]{y}}^{3}}$

Raise $\sqrt[4]{y}$ to the power of $1$ .

$\frac{{\sqrt[4]{y}}^{3}}{{\sqrt[4]{y}}^{1} {\sqrt[4]{y}}^{3}}$

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

$\frac{{\sqrt[4]{y}}^{3}}{{\sqrt[4]{y}}^{1 + 3}}$

Add $1$ and $3$ .

$\frac{{\sqrt[4]{y}}^{3}}{{\sqrt[4]{y}}^{4}}$

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

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{y}$ as $y^{\frac{1}{4}}$ .

$\frac{{\sqrt[4]{y}}^{3}}{{(y^{\frac{1}{4}})}^{4}}$

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

$\frac{{\sqrt[4]{y}}^{3}}{y^{\frac{1}{4} \cdot 4}}$

Combine $\frac{1}{4}$ and $4$ .

$\frac{{\sqrt[4]{y}}^{3}}{y^{\frac{4}{4}}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{{\sqrt[4]{y}}^{3}}{y^{\frac{4}{4}}}$

Rewrite the expression.

$\frac{{\sqrt[4]{y}}^{3}}{y^{1}}$

Simplify.

$\frac{{\sqrt[4]{y}}^{3}}{y}$

Step 10

Rewrite ${\sqrt[4]{y}}^{3}$ as ${(y^{3})}^{\frac{1}{4}}$ .

$\frac{\sqrt[4]{y^{3}}}{y}$

Simplify 20 root of (y^-8)/(y^-3)

Related Questions

Support LCMGCF.com by disabling your adblocker.