Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $b$ out of $3 b c^{5} n$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 2

Cancel the common factor of $c^{4}$ and $c^{5}$ .

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Step 2.1

Factor $c^{4}$ out of $7 b^{2} c^{4} n$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $c^{4}$ out of $3 c^{5} n$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

Cancel the common factor of $n$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

${(\frac{7 b^{2}}{3 c})}^{- 3}$

Step 4

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{3 c}{7 b^{2}})}^{3}$

Step 5

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

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Step 5.1

Apply the product rule to $\frac{3 c}{7 b^{2}}$ .

$\frac{{(3 c)}^{3}}{{(7 b^{2})}^{3}}$

Step 5.2

Apply the product rule to $3 c$ .

$\frac{3^{3} c^{3}}{{(7 b^{2})}^{3}}$

Step 5.3

Apply the product rule to $7 b^{2}$ .

$\frac{3^{3} c^{3}}{7^{3} {(b^{2})}^{3}}$

Step 6

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

$\frac{27 c^{3}}{7^{3} {(b^{2})}^{3}}$

Step 7

Simplify the denominator.

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Step 7.1

Raise $7$ to the power of $3$ .

$\frac{27 c^{3}}{343 {(b^{2})}^{3}}$

Step 7.2

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

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Step 7.2.1

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

$\frac{27 c^{3}}{343 b^{2 \cdot 3}}$

Step 7.2.2

Multiply $2$ by $3$ .

$\frac{27 c^{3}}{343 b^{6}}$