Algebra Examples

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

Step 1

Move $b^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Apply the product rule to $a^{3} b^{2}$ .

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

Step 4

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

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

Step 5

Simplify the denominator.

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Step 5.1

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

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Step 5.1.1

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

$\frac{27}{a^{3 \cdot 3} {(b^{2})}^{3}}$

Step 5.1.2

Multiply $3$ by $3$ .

$\frac{27}{a^{9} {(b^{2})}^{3}}$

Step 5.2

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

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Step 5.2.1

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

$\frac{27}{a^{9} b^{2 \cdot 3}}$

Step 5.2.2

Multiply $2$ by $3$ .

$\frac{27}{a^{9} b^{6}}$