Algebra Examples

$\frac{20 y^{2} h^{- 1}}{{(5 y^{5} h^{2})}^{2}}$

Step 1

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

$\frac{20 y^{2}}{{(5 y^{5} h^{2})}^{2} h}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $5 y^{5} h^{2}$ .

$\frac{20 y^{2}}{{(5 y^{5})}^{2} {(h^{2})}^{2} h}$

Step 2.2

Apply the product rule to $5 y^{5}$ .

$\frac{20 y^{2}}{5^{2} {(y^{5})}^{2} {(h^{2})}^{2} h}$

Step 2.3

Raise $5$ to the power of $2$ .

$\frac{20 y^{2}}{25 {(y^{5})}^{2} {(h^{2})}^{2} h}$

Step 2.4

Multiply the exponents in ${(y^{5})}^{2}$ .

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Step 2.4.1

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

$\frac{20 y^{2}}{25 y^{5 \cdot 2} {(h^{2})}^{2} h}$

Step 2.4.2

Multiply $5$ by $2$ .

$\frac{20 y^{2}}{25 y^{10} {(h^{2})}^{2} h}$

Step 2.5

Multiply the exponents in ${(h^{2})}^{2}$ .

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Step 2.5.1

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

$\frac{20 y^{2}}{25 y^{10} h^{2 \cdot 2} h}$

Step 2.5.2

Multiply $2$ by $2$ .

$\frac{20 y^{2}}{25 y^{10} h^{4} h}$

Step 2.6

Combine exponents.

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Step 2.6.1

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

$\frac{20 y^{2}}{25 y^{10} (h^{1} h^{4})}$

Step 2.6.2

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

$\frac{20 y^{2}}{25 y^{10} h^{1 + 4}}$

Step 2.6.3

Add $1$ and $4$ .

$\frac{20 y^{2}}{25 y^{10} h^{5}}$

Step 3

Cancel the common factor of $20$ and $25$ .

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Step 3.1

Factor $5$ out of $20 y^{2}$ .

$\frac{5 (4 y^{2})}{25 y^{10} h^{5}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $5$ out of $25 y^{10} h^{5}$ .

$\frac{5 (4 y^{2})}{5 (5 y^{10} h^{5})}$

Step 3.2.2

Cancel the common factor.

$\frac{5 (4 y^{2})}{5 (5 y^{10} h^{5})}$

Step 3.2.3

Rewrite the expression.

$\frac{4 y^{2}}{5 y^{10} h^{5}}$

Step 4

Cancel the common factor of $y^{2}$ and $y^{10}$ .

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Step 4.1

Factor $y^{2}$ out of $4 y^{2}$ .

$\frac{y^{2} \cdot 4}{5 y^{10} h^{5}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $y^{2}$ out of $5 y^{10} h^{5}$ .

$\frac{y^{2} \cdot 4}{y^{2} (5 y^{8} h^{5})}$

Step 4.2.2

Cancel the common factor.

$\frac{y^{2} \cdot 4}{y^{2} (5 y^{8} h^{5})}$

Step 4.2.3

Rewrite the expression.

$\frac{4}{5 y^{8} h^{5}}$