Basic Math Examples

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

Step 1

Move $b^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

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

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

Step 3

Simplify the denominator.

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Step 3.1

Apply the product rule to $a^{3} b^{4}$ .

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

Multiply $3$ by $2$ .

$\frac{1}{a^{6} {(b^{4})}^{2}}$

Step 3.3

Multiply the exponents in ${(b^{4})}^{2}$ .

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Step 3.3.1

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

$\frac{1}{a^{6} b^{4 \cdot 2}}$

Step 3.3.2

Multiply $4$ by $2$ .

$\frac{1}{a^{6} b^{8}}$