Basic Math Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

Multiply $3$ by $3$ .

$\frac{r^{3} s^{9}}{{(r^{- 2} s^{3})}^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $r^{- 2} s^{3}$ .

$\frac{r^{3} s^{9}}{{(r^{- 2})}^{2} {(s^{3})}^{2}}$

Step 2.2

Multiply the exponents in ${(r^{- 2})}^{2}$ .

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Step 2.2.1

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

$\frac{r^{3} s^{9}}{r^{- 2 \cdot 2} {(s^{3})}^{2}}$

Step 2.2.2

Multiply $- 2$ by $2$ .

$\frac{r^{3} s^{9}}{r^{- 4} {(s^{3})}^{2}}$

Step 2.3

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

$\frac{r^{3} s^{9}}{\frac{1}{r^{4}} {(s^{3})}^{2}}$

Step 2.4

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

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Step 2.4.1

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

$\frac{r^{3} s^{9}}{\frac{1}{r^{4}} s^{3 \cdot 2}}$

Step 2.4.2

Multiply $3$ by $2$ .

$\frac{r^{3} s^{9}}{\frac{1}{r^{4}} s^{6}}$

Step 3

Combine $\frac{1}{r^{4}}$ and $s^{6}$ .

$\frac{r^{3} s^{9}}{\frac{s^{6}}{r^{4}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$r^{3} s^{9} \frac{r^{4}}{s^{6}}$

Step 5

Cancel the common factor of $s^{6}$ .

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Step 5.1

Factor $s^{6}$ out of $r^{3} s^{9}$ .

$s^{6} (r^{3} s^{3}) \frac{r^{4}}{s^{6}}$

Step 5.2

Cancel the common factor.

$s^{6} (r^{3} s^{3}) \frac{r^{4}}{s^{6}}$

Step 5.3

Rewrite the expression.

$r^{3} s^{3} r^{4}$

Step 6

Multiply $r^{3}$ by $r^{4}$ by adding the exponents.

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Step 6.1

Move $r^{4}$ .

$r^{4} r^{3} s^{3}$

Step 6.2

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

$r^{4 + 3} s^{3}$

Step 6.3

Add $4$ and $3$ .

$r^{7} s^{3}$