Pre-Algebra Examples

${(\frac{4 u^{4}}{8 v^{5}})}^{6}$

Step 1

Cancel the common factor of $4$ and $8$ .

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Step 1.1

Factor $4$ out of $4 u^{4}$ .

${(\frac{4 (u^{4})}{8 v^{5}})}^{6}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $4$ out of $8 v^{5}$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

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 $\frac{u^{4}}{2 v^{5}}$ .

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

Step 2.2

Apply the product rule to $2 v^{5}$ .

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

Step 3

Multiply the exponents in ${(u^{4})}^{6}$ .

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Step 3.1

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

$\frac{u^{4 \cdot 6}}{2^{6} {(v^{5})}^{6}}$

Step 3.2

Multiply $4$ by $6$ .

$\frac{u^{24}}{2^{6} {(v^{5})}^{6}}$

Step 4

Simplify the denominator.

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Step 4.1

Raise $2$ to the power of $6$ .

$\frac{u^{24}}{64 {(v^{5})}^{6}}$

Step 4.2

Multiply the exponents in ${(v^{5})}^{6}$ .

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Step 4.2.1

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

$\frac{u^{24}}{64 v^{5 \cdot 6}}$

Step 4.2.2

Multiply $5$ by $6$ .

$\frac{u^{24}}{64 v^{30}}$