Algebra Examples

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

Step 1

Move ${(a^{3} b)}^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Simplify the denominator.

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

Multiply $3$ by $2$ .

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

Step 2.3

Multiply $a^{4}$ by $a^{6}$ by adding the exponents.

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Step 2.3.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2.3.2

Add $4$ and $6$ .

$\frac{1}{a^{10} b^{2}}$