Finite Math Examples

${(\frac{r^{- \frac{3}{4}}}{s^{- \frac{2}{3}}})}^{12}$

Step 1

Move $r^{- \frac{3}{4}}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{1}{s^{- \frac{2}{3}} r^{\frac{3}{4}}})}^{12}$

Step 2

Move $s^{- \frac{2}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{s^{\frac{2}{3}}}{r^{\frac{3}{4}}})}^{12}$

Step 3

Apply the product rule to $\frac{s^{\frac{2}{3}}}{r^{\frac{3}{4}}}$ .

$\frac{{(s^{\frac{2}{3}})}^{12}}{{(r^{\frac{3}{4}})}^{12}}$

Step 4

Multiply the exponents in ${(s^{\frac{2}{3}})}^{12}$ .

Tap for more steps...

Step 4.1

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

$\frac{s^{\frac{2}{3} \cdot 12}}{{(r^{\frac{3}{4}})}^{12}}$

Step 4.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.2.1

Factor $3$ out of $12$ .

$\frac{s^{\frac{2}{3} \cdot (3 (4))}}{{(r^{\frac{3}{4}})}^{12}}$

Step 4.2.2

Cancel the common factor.

$\frac{s^{\frac{2}{3} \cdot (3 \cdot 4)}}{{(r^{\frac{3}{4}})}^{12}}$

Step 4.2.3

Rewrite the expression.

$\frac{s^{2 \cdot 4}}{{(r^{\frac{3}{4}})}^{12}}$

Step 4.3

Multiply $2$ by $4$ .

$\frac{s^{8}}{{(r^{\frac{3}{4}})}^{12}}$

Step 5

Multiply the exponents in ${(r^{\frac{3}{4}})}^{12}$ .

Tap for more steps...

Step 5.1

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

$\frac{s^{8}}{r^{\frac{3}{4} \cdot 12}}$

Step 5.2

Cancel the common factor of $4$ .

Tap for more steps...

Step 5.2.1

Factor $4$ out of $12$ .

$\frac{s^{8}}{r^{\frac{3}{4} \cdot (4 (3))}}$

Step 5.2.2

Cancel the common factor.

$\frac{s^{8}}{r^{\frac{3}{4} \cdot (4 \cdot 3)}}$

Step 5.2.3

Rewrite the expression.

$\frac{s^{8}}{r^{3 \cdot 3}}$

Step 5.3

Multiply $3$ by $3$ .

$\frac{s^{8}}{r^{9}}$