Algebra Examples

${(\frac{- 6 r s^{- 3}}{15 r^{7} s^{- 3}})}^{2}$

Step 1

Cancel the common factor of $- 6$ and $15$ .

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Step 1.1

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

${(\frac{3 (- 2 r s^{- 3})}{15 r^{7} s^{- 3}})}^{2}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $15 r^{7} s^{- 3}$ .

${(\frac{3 (- 2 r s^{- 3})}{3 (5 r^{7} s^{- 3})})}^{2}$

Step 1.2.2

Cancel the common factor.

${(\frac{3 (- 2 r s^{- 3})}{3 (5 r^{7} s^{- 3})})}^{2}$

Step 1.2.3

Rewrite the expression.

${(\frac{- 2 r s^{- 3}}{5 r^{7} s^{- 3}})}^{2}$

Step 2

Cancel the common factor of $r$ and $r^{7}$ .

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Step 2.1

Factor $r$ out of $- 2 r s^{- 3}$ .

${(\frac{r (- 2 s^{- 3})}{5 r^{7} s^{- 3}})}^{2}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $r$ out of $5 r^{7} s^{- 3}$ .

${(\frac{r (- 2 s^{- 3})}{r (5 r^{6} s^{- 3})})}^{2}$

Step 2.2.2

Cancel the common factor.

${(\frac{r (- 2 s^{- 3})}{r (5 r^{6} s^{- 3})})}^{2}$

Step 2.2.3

Rewrite the expression.

${(\frac{- 2 s^{- 3}}{5 r^{6} s^{- 3}})}^{2}$

Step 3

Cancel the common factor of $s^{- 3}$ .

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Step 3.1

Cancel the common factor.

${(\frac{- 2 s^{- 3}}{5 r^{6} s^{- 3}})}^{2}$

Step 3.2

Rewrite the expression.

${(\frac{- 2}{5 r^{6}})}^{2}$

Step 4

Move the negative in front of the fraction.

${(- \frac{2}{5 r^{6}})}^{2}$

Step 5

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

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Step 5.1

Apply the product rule to $- \frac{2}{5 r^{6}}$ .

${(- 1)}^{2} {(\frac{2}{5 r^{6}})}^{2}$

Step 5.2

Apply the product rule to $\frac{2}{5 r^{6}}$ .

${(- 1)}^{2} \frac{2^{2}}{{(5 r^{6})}^{2}}$

Step 5.3

Apply the product rule to $5 r^{6}$ .

${(- 1)}^{2} \frac{2^{2}}{5^{2} {(r^{6})}^{2}}$

Step 6

Simplify the expression.

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Step 6.1

Raise $- 1$ to the power of $2$ .

$1 \frac{2^{2}}{5^{2} {(r^{6})}^{2}}$

Step 6.2

Multiply $\frac{2^{2}}{5^{2} {(r^{6})}^{2}}$ by $1$ .

$\frac{2^{2}}{5^{2} {(r^{6})}^{2}}$

Step 6.3

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

$\frac{4}{5^{2} {(r^{6})}^{2}}$

Step 7

Simplify the denominator.

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Step 7.1

Raise $5$ to the power of $2$ .

$\frac{4}{25 {(r^{6})}^{2}}$

Step 7.2

Multiply the exponents in ${(r^{6})}^{2}$ .

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Step 7.2.1

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

$\frac{4}{25 r^{6 \cdot 2}}$

Step 7.2.2

Multiply $6$ by $2$ .

$\frac{4}{25 r^{12}}$