Algebra Examples

$\frac{2 h^{7} v^{- 3}}{{(5 h^{- 4} v^{5})}^{- 5}}$

Step 1

Move $v^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{2 h^{7}}{{(5 h^{- 4} v^{5})}^{- 5} v^{3}}$

Step 2

Move ${(5 h^{- 4} v^{5})}^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{2 h^{7} {(5 h^{- 4} v^{5})}^{5}}{v^{3}}$

Step 3

Simplify the numerator.

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Step 3.1

Apply the product rule to $5 h^{- 4} v^{5}$ .

$\frac{2 h^{7} {(5 h^{- 4})}^{5} {(v^{5})}^{5}}{v^{3}}$

Step 3.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{2 h^{7} {(5 \frac{1}{h^{4}})}^{5} {(v^{5})}^{5}}{v^{3}}$

Step 3.3

Combine $5$ and $\frac{1}{h^{4}}$ .

$\frac{2 h^{7} {(\frac{5}{h^{4}})}^{5} {(v^{5})}^{5}}{v^{3}}$

Step 3.4

Apply the product rule to $\frac{5}{h^{4}}$ .

$\frac{2 h^{7} \frac{5^{5}}{{(h^{4})}^{5}} {(v^{5})}^{5}}{v^{3}}$

Step 3.5

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

$\frac{2 h^{7} \frac{3125}{{(h^{4})}^{5}} {(v^{5})}^{5}}{v^{3}}$

Step 3.6

Multiply the exponents in ${(h^{4})}^{5}$ .

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Step 3.6.1

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

$\frac{2 h^{7} \frac{3125}{h^{4 \cdot 5}} {(v^{5})}^{5}}{v^{3}}$

Step 3.6.2

Multiply $4$ by $5$ .

$\frac{2 h^{7} \frac{3125}{h^{20}} {(v^{5})}^{5}}{v^{3}}$

Step 3.7

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

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Step 3.7.1

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

$\frac{2 h^{7} \frac{3125}{h^{20}} v^{5 \cdot 5}}{v^{3}}$

Step 3.7.2

Multiply $5$ by $5$ .

$\frac{2 h^{7} \frac{3125}{h^{20}} v^{25}}{v^{3}}$

Step 3.8

Combine exponents.

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Step 3.8.1

Combine $2$ and $\frac{3125}{h^{20}}$ .

$\frac{h^{7} \frac{2 \cdot 3125}{h^{20}} v^{25}}{v^{3}}$

Step 3.8.2

Multiply $2$ by $3125$ .

$\frac{h^{7} \frac{6250}{h^{20}} v^{25}}{v^{3}}$

Step 3.8.3

Combine $h^{7}$ and $\frac{6250}{h^{20}}$ .

$\frac{\frac{h^{7} \cdot 6250}{h^{20}} v^{25}}{v^{3}}$

Step 3.8.4

Combine $\frac{h^{7} \cdot 6250}{h^{20}}$ and $v^{25}$ .

$\frac{\frac{h^{7} \cdot 6250 v^{25}}{h^{20}}}{v^{3}}$

Step 3.9

Reduce the expression $\frac{h^{7} \cdot 6250 v^{25}}{h^{20}}$ by cancelling the common factors.

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Step 3.9.1

Factor $h^{7}$ out of $h^{7} \cdot 6250 v^{25}$ .

$\frac{\frac{h^{7} (6250 v^{25})}{h^{20}}}{v^{3}}$

Step 3.9.2

Factor $h^{7}$ out of $h^{20}$ .

$\frac{\frac{h^{7} (6250 v^{25})}{h^{7} h^{13}}}{v^{3}}$

Step 3.9.3

Cancel the common factor.

$\frac{\frac{h^{7} (6250 v^{25})}{h^{7} h^{13}}}{v^{3}}$

Step 3.9.4

Rewrite the expression.

$\frac{\frac{6250 v^{25}}{h^{13}}}{v^{3}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{6250 v^{25}}{h^{13}} \cdot \frac{1}{v^{3}}$

Step 5

Combine.

$\frac{6250 v^{25} \cdot 1}{h^{13} v^{3}}$

Step 6

Cancel the common factor of $v^{25}$ and $v^{3}$ .

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Step 6.1

Factor $v^{3}$ out of $6250 v^{25} \cdot 1$ .

$\frac{v^{3} (6250 v^{22} \cdot 1)}{h^{13} v^{3}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $v^{3}$ out of $h^{13} v^{3}$ .

$\frac{v^{3} (6250 v^{22} \cdot 1)}{v^{3} h^{13}}$

Step 6.2.2

Cancel the common factor.

$\frac{v^{3} (6250 v^{22} \cdot 1)}{v^{3} h^{13}}$

Step 6.2.3

Rewrite the expression.

$\frac{6250 v^{22} \cdot 1}{h^{13}}$

Step 7

Multiply $6250$ by $1$ .

$\frac{6250 v^{22}}{h^{13}}$