Simplify (1/( square root of y))^(-1/5)

${(\frac{1}{\sqrt{y}})}^{\frac{- 1}{5}}$

Step 1

Multiply $\frac{1}{\sqrt{y}}$ by $\frac{\sqrt{y}}{\sqrt{y}}$ .

${(\frac{1}{\sqrt{y}} \cdot \frac{\sqrt{y}}{\sqrt{y}})}^{\frac{- 1}{5}}$

Step 2

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt{y}}$ by $\frac{\sqrt{y}}{\sqrt{y}}$ .

${(\frac{\sqrt{y}}{\sqrt{y} \sqrt{y}})}^{\frac{- 1}{5}}$

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

${(\frac{\sqrt{y}}{{\sqrt{y}}^{1} \sqrt{y}})}^{\frac{- 1}{5}}$

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

${(\frac{\sqrt{y}}{{\sqrt{y}}^{1} {\sqrt{y}}^{1}})}^{\frac{- 1}{5}}$

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

${(\frac{\sqrt{y}}{{\sqrt{y}}^{1 + 1}})}^{\frac{- 1}{5}}$

Add $1$ and $1$ .

${(\frac{\sqrt{y}}{{\sqrt{y}}^{2}})}^{\frac{- 1}{5}}$

Rewrite ${\sqrt{y}}^{2}$ as $y$ .

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

${(\frac{\sqrt{y}}{{(y^{\frac{1}{2}})}^{2}})}^{\frac{- 1}{5}}$

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

${(\frac{\sqrt{y}}{y^{\frac{1}{2} \cdot 2}})}^{\frac{- 1}{5}}$

Combine $\frac{1}{2}$ and $2$ .

${(\frac{\sqrt{y}}{y^{\frac{2}{2}}})}^{\frac{- 1}{5}}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(\frac{\sqrt{y}}{y^{\frac{2}{2}}})}^{\frac{- 1}{5}}$

Rewrite the expression.

${(\frac{\sqrt{y}}{y^{1}})}^{\frac{- 1}{5}}$

Simplify.

${(\frac{\sqrt{y}}{y})}^{\frac{- 1}{5}}$

Step 3

Move the negative in front of the fraction.

${(\frac{\sqrt{y}}{y})}^{- \frac{1}{5}}$

Step 4

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Step 5

Multiply $\frac{y}{\sqrt{y}}$ by $\frac{\sqrt{y}}{\sqrt{y}}$ .

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

Step 6

Combine and simplify the denominator.

Multiply $\frac{y}{\sqrt{y}}$ by $\frac{\sqrt{y}}{\sqrt{y}}$ .

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

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

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

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

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

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

${(\frac{y \sqrt{y}}{{\sqrt{y}}^{1 + 1}})}^{\frac{1}{5}}$

Add $1$ and $1$ .

${(\frac{y \sqrt{y}}{{\sqrt{y}}^{2}})}^{\frac{1}{5}}$

Rewrite ${\sqrt{y}}^{2}$ as $y$ .

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

${(\frac{y \sqrt{y}}{{(y^{\frac{1}{2}})}^{2}})}^{\frac{1}{5}}$

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

${(\frac{y \sqrt{y}}{y^{\frac{1}{2} \cdot 2}})}^{\frac{1}{5}}$

Combine $\frac{1}{2}$ and $2$ .

${(\frac{y \sqrt{y}}{y^{\frac{2}{2}}})}^{\frac{1}{5}}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(\frac{y \sqrt{y}}{y^{\frac{2}{2}}})}^{\frac{1}{5}}$

Rewrite the expression.

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

Simplify.

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

Step 7

Cancel the common factor of $y$ .

Cancel the common factor.

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

Divide $\sqrt{y}$ by $1$ .

${\sqrt{y}}^{\frac{1}{5}}$

Simplify (1/( square root of y))^(-1/5)

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