Algebra Examples

$\frac{5 n^{- 7} c^{4}}{- 3 {(n^{- 3} c^{2})}^{2}}$

Step 1

Move $n^{- 7}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{5 c^{4}}{- 3 {(n^{- 3} c^{2})}^{2} n^{7}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $n^{- 3} c^{2}$ .

$\frac{5 c^{4}}{- 3 {(n^{- 3})}^{2} {(c^{2})}^{2} n^{7}}$

Step 2.2

Multiply the exponents in ${(n^{- 3})}^{2}$ .

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Step 2.2.1

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

$\frac{5 c^{4}}{- 3 n^{- 3 \cdot 2} {(c^{2})}^{2} n^{7}}$

Step 2.2.2

Multiply $- 3$ by $2$ .

$\frac{5 c^{4}}{- 3 n^{- 6} {(c^{2})}^{2} n^{7}}$

Step 2.3

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

$\frac{5 c^{4}}{- 3 \frac{1}{n^{6}} {(c^{2})}^{2} n^{7}}$

Step 2.4

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

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Step 2.4.1

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

$\frac{5 c^{4}}{- 3 \frac{1}{n^{6}} c^{2 \cdot 2} n^{7}}$

Step 2.4.2

Multiply $2$ by $2$ .

$\frac{5 c^{4}}{- 3 \frac{1}{n^{6}} c^{4} n^{7}}$

Step 2.5

Combine exponents.

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Step 2.5.1

Combine $- 3$ and $\frac{1}{n^{6}}$ .

$\frac{5 c^{4}}{\frac{- 3}{n^{6}} c^{4} n^{7}}$

Step 2.5.2

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

$\frac{5 c^{4}}{\frac{- 3 c^{4}}{n^{6}} n^{7}}$

Step 2.5.3

Combine $\frac{- 3 c^{4}}{n^{6}}$ and $n^{7}$ .

$\frac{5 c^{4}}{\frac{- 3 c^{4} n^{7}}{n^{6}}}$

Step 2.6

Reduce the expression by cancelling the common factors.

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Step 2.6.1

Reduce the expression $\frac{- 3 c^{4} n^{7}}{n^{6}}$ by cancelling the common factors.

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Step 2.6.1.1

Factor $n^{6}$ out of $- 3 c^{4} n^{7}$ .

$\frac{5 c^{4}}{\frac{n^{6} (- 3 c^{4} n)}{n^{6}}}$

Step 2.6.1.2

Multiply by $1$ .

$\frac{5 c^{4}}{\frac{n^{6} (- 3 c^{4} n)}{n^{6} \cdot 1}}$

Step 2.6.1.3

Cancel the common factor.

$\frac{5 c^{4}}{\frac{n^{6} (- 3 c^{4} n)}{n^{6} \cdot 1}}$

Step 2.6.1.4

Rewrite the expression.

$\frac{5 c^{4}}{\frac{- 3 c^{4} n}{1}}$

Step 2.6.2

Divide $- 3 c^{4} n$ by $1$ .

$\frac{5 c^{4}}{- 3 c^{4} n}$

Step 3

Cancel the common factor of $c^{4}$ .

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Step 3.1

Cancel the common factor.

$\frac{5 c^{4}}{- 3 c^{4} n}$

Step 3.2

Rewrite the expression.

$\frac{5}{- 3 n}$

Step 4

Move the negative in front of the fraction.

$- \frac{5}{3 n}$