Finite Math Examples

${(\frac{3 r^{9} s^{- 4}}{4 r^{- 3} s^{5}})}^{- 3}$

Step 1

Move $s^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{3 r^{9}}{4 r^{- 3} s^{5} s^{4}})}^{- 3}$

Step 2

Multiply $s^{5}$ by $s^{4}$ by adding the exponents.

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Step 2.1

Move $s^{4}$ .

${(\frac{3 r^{9}}{4 r^{- 3} (s^{4} s^{5})})}^{- 3}$

Step 2.2

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

${(\frac{3 r^{9}}{4 r^{- 3} s^{4 + 5}})}^{- 3}$

Step 2.3

Add $4$ and $5$ .

${(\frac{3 r^{9}}{4 r^{- 3} s^{9}})}^{- 3}$

Step 3

Move $r^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{3 r^{9} r^{3}}{4 s^{9}})}^{- 3}$

Step 4

Multiply $r^{9}$ by $r^{3}$ by adding the exponents.

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Step 4.1

Move $r^{3}$ .

${(\frac{3 (r^{3} r^{9})}{4 s^{9}})}^{- 3}$

Step 4.2

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

${(\frac{3 r^{3 + 9}}{4 s^{9}})}^{- 3}$

Step 4.3

Add $3$ and $9$ .

${(\frac{3 r^{12}}{4 s^{9}})}^{- 3}$

Step 5

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

${(\frac{4 s^{9}}{3 r^{12}})}^{3}$

Step 6

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

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Step 6.1

Apply the product rule to $\frac{4 s^{9}}{3 r^{12}}$ .

$\frac{{(4 s^{9})}^{3}}{{(3 r^{12})}^{3}}$

Step 6.2

Apply the product rule to $4 s^{9}$ .

$\frac{4^{3} {(s^{9})}^{3}}{{(3 r^{12})}^{3}}$

Step 6.3

Apply the product rule to $3 r^{12}$ .

$\frac{4^{3} {(s^{9})}^{3}}{3^{3} {(r^{12})}^{3}}$

Step 7

Simplify the numerator.

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Step 7.1

Raise $4$ to the power of $3$ .

$\frac{64 {(s^{9})}^{3}}{3^{3} {(r^{12})}^{3}}$

Step 7.2

Multiply the exponents in ${(s^{9})}^{3}$ .

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Step 7.2.1

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

$\frac{64 s^{9 \cdot 3}}{3^{3} {(r^{12})}^{3}}$

Step 7.2.2

Multiply $9$ by $3$ .

$\frac{64 s^{27}}{3^{3} {(r^{12})}^{3}}$

Step 8

Simplify the denominator.

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Step 8.1

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

$\frac{64 s^{27}}{27 {(r^{12})}^{3}}$

Step 8.2

Multiply the exponents in ${(r^{12})}^{3}$ .

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Step 8.2.1

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

$\frac{64 s^{27}}{27 r^{12 \cdot 3}}$

Step 8.2.2

Multiply $12$ by $3$ .

$\frac{64 s^{27}}{27 r^{36}}$