Basic Math Examples

$\frac{- 2 n y^{- 2}}{\sqrt{n y^{2}}}$

Step 1

Move $y^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 2 n}{\sqrt{n y^{2}} y^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Reorder $n$ and $y^{2}$ .

$\frac{- 2 n}{\sqrt{y^{2} n} y^{2}}$

Step 2.2

Pull terms out from under the radical.

$\frac{- 2 n}{y \sqrt{n} y^{2}}$

Step 2.3

Multiply $y$ by $y^{2}$ by adding the exponents.

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Step 2.3.1

Move $y^{2}$ .

$\frac{- 2 n}{y^{2} y \sqrt{n}}$

Step 2.3.2

Multiply $y^{2}$ by $y$ .

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Step 2.3.2.1

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

$\frac{- 2 n}{y^{2} y^{1} \sqrt{n}}$

Step 2.3.2.2

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

$\frac{- 2 n}{y^{2 + 1} \sqrt{n}}$

Step 2.3.3

Add $2$ and $1$ .

$\frac{- 2 n}{y^{3} \sqrt{n}}$

Step 3

Move the negative in front of the fraction.

$- \frac{2 n}{y^{3} \sqrt{n}}$

Step 4

Multiply $\frac{2 n}{y^{3} \sqrt{n}}$ by $\frac{\sqrt{n}}{\sqrt{n}}$ .

$- (\frac{2 n}{y^{3} \sqrt{n}} \cdot \frac{\sqrt{n}}{\sqrt{n}})$

Step 5

Combine and simplify the denominator.

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Step 5.1

Multiply $\frac{2 n}{y^{3} \sqrt{n}}$ by $\frac{\sqrt{n}}{\sqrt{n}}$ .

$- \frac{2 n \sqrt{n}}{y^{3} \sqrt{n} \sqrt{n}}$

Step 5.2

Move $\sqrt{n}$ .

$- \frac{2 n \sqrt{n}}{y^{3} (\sqrt{n} \sqrt{n})}$

Step 5.3

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

$- \frac{2 n \sqrt{n}}{y^{3} ({\sqrt{n}}^{1} \sqrt{n})}$

Step 5.4

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

$- \frac{2 n \sqrt{n}}{y^{3} ({\sqrt{n}}^{1} {\sqrt{n}}^{1})}$

Step 5.5

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

$- \frac{2 n \sqrt{n}}{y^{3} {\sqrt{n}}^{1 + 1}}$

Step 5.6

Add $1$ and $1$ .

$- \frac{2 n \sqrt{n}}{y^{3} {\sqrt{n}}^{2}}$

Step 5.7

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

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Step 5.7.1

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

$- \frac{2 n \sqrt{n}}{y^{3} {(n^{\frac{1}{2}})}^{2}}$

Step 5.7.2

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

$- \frac{2 n \sqrt{n}}{y^{3} n^{\frac{1}{2} \cdot 2}}$

Step 5.7.3

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

$- \frac{2 n \sqrt{n}}{y^{3} n^{\frac{2}{2}}}$

Step 5.7.4

Cancel the common factor of $2$ .

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Step 5.7.4.1

Cancel the common factor.

$- \frac{2 n \sqrt{n}}{y^{3} n^{\frac{2}{2}}}$

Step 5.7.4.2

Rewrite the expression.

$- \frac{2 n \sqrt{n}}{y^{3} n^{1}}$

Step 5.7.5

Simplify.

$- \frac{2 n \sqrt{n}}{y^{3} n}$

Step 6

Cancel the common factor of $n$ .

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Step 6.1

Cancel the common factor.

$- \frac{2 n \sqrt{n}}{y^{3} n}$

Step 6.2

Rewrite the expression.

$- \frac{2 \sqrt{n}}{y^{3}}$