Finite Math Examples

$\frac{{(5 v^{2})}^{3}}{{(2 v)}^{4}}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{5^{3} {(v^{2})}^{3}}{{(2 v)}^{4}}$

Step 1.2

Raise $5$ to the power of $3$ .

$\frac{125 {(v^{2})}^{3}}{{(2 v)}^{4}}$

Step 1.3

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

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Step 1.3.1

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

$\frac{125 v^{2 \cdot 3}}{{(2 v)}^{4}}$

Step 1.3.2

Multiply $2$ by $3$ .

$\frac{125 v^{6}}{{(2 v)}^{4}}$

$\frac{125 v^{6}}{{(2 v)}^{4}}$

$\frac{125 v^{6}}{{(2 v)}^{4}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $2 v$ .

$\frac{125 v^{6}}{2^{4} v^{4}}$

Step 2.2

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

$\frac{125 v^{6}}{16 v^{4}}$

$\frac{125 v^{6}}{16 v^{4}}$

Step 3

Cancel the common factor of $v^{6}$ and $v^{4}$ .

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Step 3.1

Factor $v^{4}$ out of $125 v^{6}$ .

$\frac{v^{4} (125 v^{2})}{16 v^{4}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $v^{4}$ out of $16 v^{4}$ .

$\frac{v^{4} (125 v^{2})}{v^{4} \cdot 16}$

Step 3.2.2

Cancel the common factor.

$\frac{v^{4} (125 v^{2})}{v^{4} \cdot 16}$

Step 3.2.3

Rewrite the expression.

$\frac{125 v^{2}}{16}$

$\frac{125 v^{2}}{16}$

$\frac{125 v^{2}}{16}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$