Pre-Algebra Examples

${(\frac{- 4 p q}{r^{3}})}^{2}$

Step 1

Move the negative in front of the fraction.

${(- \frac{4 p q}{r^{3}})}^{2}$

Step 2

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

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Step 2.1

Apply the product rule to $- \frac{4 p q}{r^{3}}$ .

${(- 1)}^{2} {(\frac{4 p q}{r^{3}})}^{2}$

Step 2.2

Apply the product rule to $\frac{4 p q}{r^{3}}$ .

${(- 1)}^{2} \frac{{(4 p q)}^{2}}{{(r^{3})}^{2}}$

Step 2.3

Apply the product rule to $4 p q$ .

${(- 1)}^{2} \frac{{(4 p)}^{2} q^{2}}{{(r^{3})}^{2}}$

Step 2.4

Apply the product rule to $4 p$ .

${(- 1)}^{2} \frac{4^{2} p^{2} q^{2}}{{(r^{3})}^{2}}$

Step 3

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

$1 \frac{4^{2} p^{2} q^{2}}{{(r^{3})}^{2}}$

Step 4

Multiply $\frac{4^{2} p^{2} q^{2}}{{(r^{3})}^{2}}$ by $1$ .

$\frac{4^{2} p^{2} q^{2}}{{(r^{3})}^{2}}$

Step 5

Raise $4$ to the power of $2$ .

$\frac{16 p^{2} q^{2}}{{(r^{3})}^{2}}$

Step 6

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

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Step 6.1

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

$\frac{16 p^{2} q^{2}}{r^{3 \cdot 2}}$

Step 6.2

Multiply $3$ by $2$ .

$\frac{16 p^{2} q^{2}}{r^{6}}$