Algebra Examples

$\frac{6 h^{10} u^{4}}{{(- 2 h^{- 4} u^{3})}^{3}}$

Step 1

Simplify the denominator.

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Step 1.1

Apply the product rule to $- 2 h^{- 4} u^{3}$ .

$\frac{6 h^{10} u^{4}}{{(- 2 h^{- 4})}^{3} {(u^{3})}^{3}}$

Step 1.2

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

$\frac{6 h^{10} u^{4}}{{(- 2 \frac{1}{h^{4}})}^{3} {(u^{3})}^{3}}$

Step 1.3

Combine $- 2$ and $\frac{1}{h^{4}}$ .

$\frac{6 h^{10} u^{4}}{{(\frac{- 2}{h^{4}})}^{3} {(u^{3})}^{3}}$

Step 1.4

Move the negative in front of the fraction.

$\frac{6 h^{10} u^{4}}{{(- \frac{2}{h^{4}})}^{3} {(u^{3})}^{3}}$

Step 1.5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.5.1

Apply the product rule to $- \frac{2}{h^{4}}$ .

$\frac{6 h^{10} u^{4}}{{(- 1)}^{3} {(\frac{2}{h^{4}})}^{3} {(u^{3})}^{3}}$

Step 1.5.2

Apply the product rule to $\frac{2}{h^{4}}$ .

$\frac{6 h^{10} u^{4}}{{(- 1)}^{3} \frac{2^{3}}{{(h^{4})}^{3}} {(u^{3})}^{3}}$

Step 1.6

Raise $- 1$ to the power of $3$ .

$\frac{6 h^{10} u^{4}}{- \frac{2^{3}}{{(h^{4})}^{3}} {(u^{3})}^{3}}$

Step 1.7

Raise $2$ to the power of $3$ .

$\frac{6 h^{10} u^{4}}{- \frac{8}{{(h^{4})}^{3}} {(u^{3})}^{3}}$

Step 1.8

Multiply the exponents in ${(h^{4})}^{3}$ .

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Step 1.8.1

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

$\frac{6 h^{10} u^{4}}{- \frac{8}{h^{4 \cdot 3}} {(u^{3})}^{3}}$

Step 1.8.2

Multiply $4$ by $3$ .

$\frac{6 h^{10} u^{4}}{- \frac{8}{h^{12}} {(u^{3})}^{3}}$

Step 1.9

Multiply the exponents in ${(u^{3})}^{3}$ .

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Step 1.9.1

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

$\frac{6 h^{10} u^{4}}{- \frac{8}{h^{12}} u^{3 \cdot 3}}$

Step 1.9.2

Multiply $3$ by $3$ .

$\frac{6 h^{10} u^{4}}{- \frac{8}{h^{12}} u^{9}}$

Step 1.10

Combine $u^{9}$ and $\frac{8}{h^{12}}$ .

$\frac{6 h^{10} u^{4}}{- \frac{u^{9} \cdot 8}{h^{12}}}$

Step 1.11

Move $8$ to the left of $u^{9}$ .

$\frac{6 h^{10} u^{4}}{- \frac{8 u^{9}}{h^{12}}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$6 h^{10} u^{4} (- \frac{h^{12}}{8 u^{9}})$

Step 3

Cancel the common factor of $2 u^{4}$ .

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Step 3.1

Move the leading negative in $- \frac{h^{12}}{8 u^{9}}$ into the numerator.

$6 h^{10} u^{4} \frac{- h^{12}}{8 u^{9}}$

Step 3.2

Factor $2 u^{4}$ out of $6 h^{10} u^{4}$ .

$2 u^{4} (3 h^{10}) \frac{- h^{12}}{8 u^{9}}$

Step 3.3

Factor $2 u^{4}$ out of $8 u^{9}$ .

$2 u^{4} (3 h^{10}) \frac{- h^{12}}{2 u^{4} (4 u^{5})}$

Step 3.4

Cancel the common factor.

$2 u^{4} (3 h^{10}) \frac{- h^{12}}{2 u^{4} (4 u^{5})}$

Step 3.5

Rewrite the expression.

$3 h^{10} \frac{- h^{12}}{4 u^{5}}$

Step 4

Combine $3$ and $\frac{- h^{12}}{4 u^{5}}$ .

$h^{10} \frac{3 (- h^{12})}{4 u^{5}}$

Step 5

Multiply $- 1$ by $3$ .

$h^{10} \frac{- 3 h^{12}}{4 u^{5}}$

Step 6

Combine $h^{10}$ and $\frac{- 3 h^{12}}{4 u^{5}}$ .

$\frac{h^{10} (- 3 h^{12})}{4 u^{5}}$

Step 7

Multiply $h^{10}$ by $h^{12}$ by adding the exponents.

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Step 7.1

Move $h^{12}$ .

$\frac{h^{12} h^{10} \cdot - 3}{4 u^{5}}$

Step 7.2

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

$\frac{h^{12 + 10} \cdot - 3}{4 u^{5}}$

Step 7.3

Add $12$ and $10$ .

$\frac{h^{22} \cdot - 3}{4 u^{5}}$

Step 8

Move $- 3$ to the left of $h^{22}$ .

$\frac{- 3 \cdot h^{22}}{4 u^{5}}$

Step 9

Move the negative in front of the fraction.

$- \frac{3 h^{22}}{4 u^{5}}$