Finite Math Examples

$\frac{u^{0} v^{- \frac{3}{2}}}{{(v u^{- 1})}^{0} \cdot (u^{\frac{1}{3}} v^{2})}$

Step 1

Move $u^{0}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{v^{- \frac{3}{2}}}{{(v u^{- 1})}^{0} \cdot (u^{\frac{1}{3}} v^{2}) u^{0}}$

Step 2

Move $v^{- \frac{3}{2}}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(v u^{- 1})}^{0} \cdot (u^{\frac{1}{3}} v^{2}) u^{0} v^{\frac{3}{2}}}$

Step 3

Simplify the denominator.

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Step 3.1

Multiply $u^{\frac{1}{3}}$ by $u^{0}$ by adding the exponents.

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Step 3.1.1

Move $u^{0}$ .

$\frac{1}{{(v u^{- 1})}^{0} \cdot (u^{0} u^{\frac{1}{3}} v^{2}) v^{\frac{3}{2}}}$

Step 3.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{{(v u^{- 1})}^{0} \cdot (u^{0 + \frac{1}{3}} v^{2}) v^{\frac{3}{2}}}$

Step 3.1.3

Add $0$ and $\frac{1}{3}$ .

$\frac{1}{{(v u^{- 1})}^{0} \cdot (u^{\frac{1}{3}} v^{2}) v^{\frac{3}{2}}}$

Step 3.2

Simplify ${(v u^{- 1})}^{0} \cdot (u^{\frac{1}{3}} v^{2})$ .

$\frac{1}{u^{\frac{1}{3}} v^{2} v^{\frac{3}{2}}}$

Step 3.3

Multiply $v^{2}$ by $v^{\frac{3}{2}}$ by adding the exponents.

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Step 3.3.1

Move $v^{\frac{3}{2}}$ .

$\frac{1}{u^{\frac{1}{3}} (v^{\frac{3}{2}} v^{2})}$

Step 3.3.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{u^{\frac{1}{3}} v^{\frac{3}{2} + 2}}$

Step 3.3.3

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{u^{\frac{1}{3}} v^{\frac{3}{2} + 2 \cdot \frac{2}{2}}}$

Step 3.3.4

Combine $2$ and $\frac{2}{2}$ .

$\frac{1}{u^{\frac{1}{3}} v^{\frac{3}{2} + \frac{2 \cdot 2}{2}}}$

Step 3.3.5

Combine the numerators over the common denominator.

$\frac{1}{u^{\frac{1}{3}} v^{\frac{3 + 2 \cdot 2}{2}}}$

Step 3.3.6

Simplify the numerator.

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Step 3.3.6.1

Multiply $2$ by $2$ .

$\frac{1}{u^{\frac{1}{3}} v^{\frac{3 + 4}{2}}}$

Step 3.3.6.2

Add $3$ and $4$ .

$\frac{1}{u^{\frac{1}{3}} v^{\frac{7}{2}}}$