Pre-Algebra Examples

${(\frac{v^{4}}{- 8 u^{2}})}^{2}$

Step 1

Move the negative in front of the fraction.

${(- \frac{v^{4}}{8 u^{2}})}^{2}$

Step 2

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

Tap for more steps...

Step 2.1

Apply the product rule to $- \frac{v^{4}}{8 u^{2}}$ .

${(- 1)}^{2} {(\frac{v^{4}}{8 u^{2}})}^{2}$

Step 2.2

Apply the product rule to $\frac{v^{4}}{8 u^{2}}$ .

${(- 1)}^{2} \frac{{(v^{4})}^{2}}{{(8 u^{2})}^{2}}$

Step 2.3

Apply the product rule to $8 u^{2}$ .

${(- 1)}^{2} \frac{{(v^{4})}^{2}}{8^{2} {(u^{2})}^{2}}$

Step 3

Simplify the expression.

Tap for more steps...

Step 3.1

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

$1 \frac{{(v^{4})}^{2}}{8^{2} {(u^{2})}^{2}}$

Step 3.2

Multiply $\frac{{(v^{4})}^{2}}{8^{2} {(u^{2})}^{2}}$ by $1$ .

$\frac{{(v^{4})}^{2}}{8^{2} {(u^{2})}^{2}}$

Step 3.3

Multiply the exponents in ${(v^{4})}^{2}$ .

Tap for more steps...

Step 3.3.1

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

$\frac{v^{4 \cdot 2}}{8^{2} {(u^{2})}^{2}}$

Step 3.3.2

Multiply $4$ by $2$ .

$\frac{v^{8}}{8^{2} {(u^{2})}^{2}}$

Step 4

Simplify the denominator.

Tap for more steps...

Step 4.1

Raise $8$ to the power of $2$ .

$\frac{v^{8}}{64 {(u^{2})}^{2}}$

Step 4.2

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

Tap for more steps...

Step 4.2.1

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

$\frac{v^{8}}{64 u^{2 \cdot 2}}$

Step 4.2.2

Multiply $2$ by $2$ .

$\frac{v^{8}}{64 u^{4}}$