Pre-Algebra Examples

${(\frac{2 u^{6}}{6 v^{2}})}^{2}$

Step 1

Cancel the common factor of $2$ and $6$ .

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Step 1.1

Factor $2$ out of $2 u^{6}$ .

${(\frac{2 (u^{6})}{6 v^{2}})}^{2}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $6 v^{2}$ .

${(\frac{2 (u^{6})}{2 (3 v^{2})})}^{2}$

Step 1.2.2

Cancel the common factor.

${(\frac{2 u^{6}}{2 (3 v^{2})})}^{2}$

Step 1.2.3

Rewrite the expression.

${(\frac{u^{6}}{3 v^{2}})}^{2}$

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 $\frac{u^{6}}{3 v^{2}}$ .

$\frac{{(u^{6})}^{2}}{{(3 v^{2})}^{2}}$

Step 2.2

Apply the product rule to $3 v^{2}$ .

$\frac{{(u^{6})}^{2}}{3^{2} {(v^{2})}^{2}}$

Step 3

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

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Step 3.1

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

$\frac{u^{6 \cdot 2}}{3^{2} {(v^{2})}^{2}}$

Step 3.2

Multiply $6$ by $2$ .

$\frac{u^{12}}{3^{2} {(v^{2})}^{2}}$

Step 4

Simplify the denominator.

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Step 4.1

Raise $3$ to the power of $2$ .

$\frac{u^{12}}{9 {(v^{2})}^{2}}$

Step 4.2

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

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Step 4.2.1

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

$\frac{u^{12}}{9 v^{2 \cdot 2}}$

Step 4.2.2

Multiply $2$ by $2$ .

$\frac{u^{12}}{9 v^{4}}$