Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 2

Simplify the numerator.

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

Multiply $2$ by $3$ .

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

Step 2.2

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

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Step 2.2.1

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

$\frac{a^{6} b^{3 \cdot 3}}{c^{3}}$

Step 2.2.2

Multiply $3$ by $3$ .

$\frac{a^{6} b^{9}}{c^{3}}$