Finite Math Examples

${(\frac{- 3^{2} a b^{3}}{c^{5}})}^{3}$

Step 1

Simplify the numerator.

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Step 1.1

Raise $3$ to the power of $2$ .

${(\frac{- 1 \cdot 9 a b^{3}}{c^{5}})}^{3}$

Step 1.2

Multiply $- 1$ by $9$ .

${(\frac{- 9 a b^{3}}{c^{5}})}^{3}$

Step 2

Move the negative in front of the fraction.

${(- \frac{9 a b^{3}}{c^{5}})}^{3}$

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 $- \frac{9 a b^{3}}{c^{5}}$ .

${(- 1)}^{3} {(\frac{9 a b^{3}}{c^{5}})}^{3}$

Step 3.2

Apply the product rule to $\frac{9 a b^{3}}{c^{5}}$ .

${(- 1)}^{3} \frac{{(9 a b^{3})}^{3}}{{(c^{5})}^{3}}$

Step 3.3

Apply the product rule to $9 a b^{3}$ .

${(- 1)}^{3} \frac{{(9 a)}^{3} {(b^{3})}^{3}}{{(c^{5})}^{3}}$

Step 3.4

Apply the product rule to $9 a$ .

${(- 1)}^{3} \frac{9^{3} a^{3} {(b^{3})}^{3}}{{(c^{5})}^{3}}$

Step 4

Raise $- 1$ to the power of $3$ .

$- \frac{9^{3} a^{3} {(b^{3})}^{3}}{{(c^{5})}^{3}}$

Step 5

Simplify the numerator.

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Step 5.1

Raise $9$ to the power of $3$ .

$- \frac{729 a^{3} {(b^{3})}^{3}}{{(c^{5})}^{3}}$

Step 5.2

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

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Step 5.2.1

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

$- \frac{729 a^{3} b^{3 \cdot 3}}{{(c^{5})}^{3}}$

Step 5.2.2

Multiply $3$ by $3$ .

$- \frac{729 a^{3} b^{9}}{{(c^{5})}^{3}}$

Step 6

Multiply the exponents in ${(c^{5})}^{3}$ .

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Step 6.1

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

$- \frac{729 a^{3} b^{9}}{c^{5 \cdot 3}}$

Step 6.2

Multiply $5$ by $3$ .

$- \frac{729 a^{3} b^{9}}{c^{15}}$