Finite Math Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Apply the product rule to $2 u^{4}$ .

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

Step 2

Multiply the exponents in ${(v^{2})}^{5}$ .

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Step 2.1

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

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

Step 2.2

Multiply $2$ by $5$ .

$\frac{v^{10}}{2^{5} {(u^{4})}^{5}}$

Step 3

Simplify the denominator.

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Step 3.1

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

$\frac{v^{10}}{32 {(u^{4})}^{5}}$

Step 3.2

Multiply the exponents in ${(u^{4})}^{5}$ .

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Step 3.2.1

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

$\frac{v^{10}}{32 u^{4 \cdot 5}}$

Step 3.2.2

Multiply $4$ by $5$ .

$\frac{v^{10}}{32 u^{20}}$