Algebra Examples

$\frac{- 3 {(u^{3} c^{- 5})}^{- 3}}{2 u^{- 5} c^{9}}$

Step 1

Simplify.

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Step 1.1

Move ${(u^{3} c^{- 5})}^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 3}{2 u^{- 5} c^{9} {(u^{3} c^{- 5})}^{3}}$

Step 1.2

Move $u^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 3 u^{5}}{2 c^{9} {(u^{3} c^{- 5})}^{3}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $u^{3} c^{- 5}$ .

$\frac{- 3 u^{5}}{2 c^{9} {(u^{3})}^{3} {(c^{- 5})}^{3}}$

Step 2.2

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

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Step 2.2.1

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

$\frac{- 3 u^{5}}{2 c^{9} u^{3 \cdot 3} {(c^{- 5})}^{3}}$

Step 2.2.2

Multiply $3$ by $3$ .

$\frac{- 3 u^{5}}{2 c^{9} u^{9} {(c^{- 5})}^{3}}$

Step 2.3

Multiply the exponents in ${(c^{- 5})}^{3}$ .

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Step 2.3.1

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

$\frac{- 3 u^{5}}{2 c^{9} u^{9} c^{- 5 \cdot 3}}$

Step 2.3.2

Multiply $- 5$ by $3$ .

$\frac{- 3 u^{5}}{2 c^{9} u^{9} c^{- 15}}$

Step 2.4

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

$\frac{- 3 u^{5}}{2 c^{9} u^{9} \frac{1}{c^{15}}}$

Step 2.5

Combine exponents.

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Step 2.5.1

Combine $2$ and $\frac{1}{c^{15}}$ .

$\frac{- 3 u^{5}}{c^{9} u^{9} \frac{2}{c^{15}}}$

Step 2.5.2

Combine $c^{9}$ and $\frac{2}{c^{15}}$ .

$\frac{- 3 u^{5}}{u^{9} \frac{c^{9} \cdot 2}{c^{15}}}$

Step 2.5.3

Combine $u^{9}$ and $\frac{c^{9} \cdot 2}{c^{15}}$ .

$\frac{- 3 u^{5}}{\frac{u^{9} (c^{9} \cdot 2)}{c^{15}}}$

Step 2.6

Remove unnecessary parentheses.

$\frac{- 3 u^{5}}{\frac{u^{9} c^{9} \cdot 2}{c^{15}}}$

Step 2.7

Reduce the expression $\frac{u^{9} c^{9} \cdot 2}{c^{15}}$ by cancelling the common factors.

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Step 2.7.1

Factor $c^{9}$ out of $u^{9} c^{9} \cdot 2$ .

$\frac{- 3 u^{5}}{\frac{c^{9} (u^{9} \cdot 2)}{c^{15}}}$

Step 2.7.2

Factor $c^{9}$ out of $c^{15}$ .

$\frac{- 3 u^{5}}{\frac{c^{9} (u^{9} \cdot 2)}{c^{9} c^{6}}}$

Step 2.7.3

Cancel the common factor.

$\frac{- 3 u^{5}}{\frac{c^{9} (u^{9} \cdot 2)}{c^{9} c^{6}}}$

Step 2.7.4

Rewrite the expression.

$\frac{- 3 u^{5}}{\frac{u^{9} \cdot 2}{c^{6}}}$

Step 2.8

Move $2$ to the left of $u^{9}$ .

$\frac{- 3 u^{5}}{\frac{2 u^{9}}{c^{6}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$- 3 u^{5} \frac{c^{6}}{2 u^{9}}$

Step 4

Cancel the common factor of $u^{5}$ .

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Step 4.1

Factor $u^{5}$ out of $- 3 u^{5}$ .

$u^{5} \cdot - 3 \frac{c^{6}}{2 u^{9}}$

Step 4.2

Factor $u^{5}$ out of $2 u^{9}$ .

$u^{5} \cdot - 3 \frac{c^{6}}{u^{5} (2 u^{4})}$

Step 4.3

Cancel the common factor.

$u^{5} \cdot - 3 \frac{c^{6}}{u^{5} (2 u^{4})}$

Step 4.4

Rewrite the expression.

$- 3 \frac{c^{6}}{2 u^{4}}$

Step 5

Combine $- 3$ and $\frac{c^{6}}{2 u^{4}}$ .

$\frac{- 3 c^{6}}{2 u^{4}}$

Step 6

Move the negative in front of the fraction.

$- \frac{3 c^{6}}{2 u^{4}}$