Basic Math Examples

${(- 2 a^{2} b^{- 4})}^{3}$

Step 1

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

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

Step 2

Multiply $- 2 a^{2} \frac{1}{b^{4}}$ .

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Step 2.1

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

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

Step 2.2

Combine $a^{2}$ and $\frac{- 2}{b^{4}}$ .

${(\frac{a^{2} \cdot - 2}{b^{4}})}^{3}$

Step 3

Move $- 2$ to the left of $a^{2}$ .

${(\frac{- 2 \cdot a^{2}}{b^{4}})}^{3}$

Step 4

Move the negative in front of the fraction.

${(- \frac{2 \cdot a^{2}}{b^{4}})}^{3}$

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 $- \frac{2 a^{2}}{b^{4}}$ .

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

Step 5.2

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

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

Step 5.3

Apply the product rule to $2 a^{2}$ .

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

Step 6

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

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

Step 7

Simplify the numerator.

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Step 7.1

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

$- \frac{8 {(a^{2})}^{3}}{{(b^{4})}^{3}}$

Step 7.2

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

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Step 7.2.1

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

$- \frac{8 a^{2 \cdot 3}}{{(b^{4})}^{3}}$

Step 7.2.2

Multiply $2$ by $3$ .

$- \frac{8 a^{6}}{{(b^{4})}^{3}}$

Step 8

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

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Step 8.1

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

$- \frac{8 a^{6}}{b^{4 \cdot 3}}$

Step 8.2

Multiply $4$ by $3$ .

$- \frac{8 a^{6}}{b^{12}}$