Pre-Algebra Examples

${(3 b^{- 2} c^{3})}^{3}$

Step 1

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

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

Step 2

Combine $3$ and $\frac{1}{b^{2}}$ .

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

Step 3

Combine $\frac{3}{b^{2}}$ and $c^{3}$ .

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Apply the product rule to $3 c^{3}$ .

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

Step 5

Simplify the numerator.

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Step 5.1

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

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

Step 5.2

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

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Step 5.2.1

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

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

Step 5.2.2

Multiply $3$ by $3$ .

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

Step 6

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

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Step 6.1

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

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

Step 6.2

Multiply $2$ by $3$ .

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