Basic Math Examples

${(3 b^{- 4} c^{- 2})}^{6} c^{3}$

Step 1

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

${(3 \frac{1}{b^{4}} c^{- 2})}^{6} c^{3}$

Step 2

Combine $3$ and $\frac{1}{b^{4}}$ .

${(\frac{3}{b^{4}} c^{- 2})}^{6} c^{3}$

Step 3

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

${(\frac{3}{b^{4}} \cdot \frac{1}{c^{2}})}^{6} c^{3}$

Step 4

Combine.

${(\frac{3 \cdot 1}{b^{4} c^{2}})}^{6} c^{3}$

Step 5

Multiply $3$ by $1$ .

${(\frac{3}{b^{4} c^{2}})}^{6} c^{3}$

Step 6

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

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Step 6.1

Apply the product rule to $\frac{3}{b^{4} c^{2}}$ .

$\frac{3^{6}}{{(b^{4} c^{2})}^{6}} c^{3}$

Step 6.2

Apply the product rule to $b^{4} c^{2}$ .

$\frac{3^{6}}{{(b^{4})}^{6} {(c^{2})}^{6}} c^{3}$

Step 7

Raise $3$ to the power of $6$ .

$\frac{729}{{(b^{4})}^{6} {(c^{2})}^{6}} c^{3}$

Step 8

Simplify the denominator.

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Step 8.1

Multiply the exponents in ${(b^{4})}^{6}$ .

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Step 8.1.1

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

$\frac{729}{b^{4 \cdot 6} {(c^{2})}^{6}} c^{3}$

Step 8.1.2

Multiply $4$ by $6$ .

$\frac{729}{b^{24} {(c^{2})}^{6}} c^{3}$

Step 8.2

Multiply the exponents in ${(c^{2})}^{6}$ .

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Step 8.2.1

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

$\frac{729}{b^{24} c^{2 \cdot 6}} c^{3}$

Step 8.2.2

Multiply $2$ by $6$ .

$\frac{729}{b^{24} c^{12}} c^{3}$

Step 9

Cancel the common factor of $c^{3}$ .

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Step 9.1

Factor $c^{3}$ out of $b^{24} c^{12}$ .

$\frac{729}{c^{3} (b^{24} c^{9})} c^{3}$

Step 9.2

Cancel the common factor.

$\frac{729}{c^{3} (b^{24} c^{9})} c^{3}$

Step 9.3

Rewrite the expression.

$\frac{729}{b^{24} c^{9}}$