Finite Math Examples

$x^{\frac{3}{4}} x^{\frac{1}{3}} x^{\frac{- 1}{2}}$

Step 1

Multiply $x^{\frac{3}{4}}$ by $x^{\frac{1}{3}}$ by adding the exponents.

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Step 1.1

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

$x^{\frac{3}{4} + \frac{1}{3}} x^{\frac{- 1}{2}}$

Step 1.2

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x^{\frac{3}{4} \cdot \frac{3}{3} + \frac{1}{3}} x^{\frac{- 1}{2}}$

Step 1.3

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$x^{\frac{3}{4} \cdot \frac{3}{3} + \frac{1}{3} \cdot \frac{4}{4}} x^{\frac{- 1}{2}}$

Step 1.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{3}{4}$ by $\frac{3}{3}$ .

$x^{\frac{3 \cdot 3}{4 \cdot 3} + \frac{1}{3} \cdot \frac{4}{4}} x^{\frac{- 1}{2}}$

Step 1.4.2

Multiply $4$ by $3$ .

$x^{\frac{3 \cdot 3}{12} + \frac{1}{3} \cdot \frac{4}{4}} x^{\frac{- 1}{2}}$

Step 1.4.3

Multiply $\frac{1}{3}$ by $\frac{4}{4}$ .

$x^{\frac{3 \cdot 3}{12} + \frac{4}{3 \cdot 4}} x^{\frac{- 1}{2}}$

Step 1.4.4

Multiply $3$ by $4$ .

$x^{\frac{3 \cdot 3}{12} + \frac{4}{12}} x^{\frac{- 1}{2}}$

Step 1.5

Combine the numerators over the common denominator.

$x^{\frac{3 \cdot 3 + 4}{12}} x^{\frac{- 1}{2}}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $3$ by $3$ .

$x^{\frac{9 + 4}{12}} x^{\frac{- 1}{2}}$

Step 1.6.2

Add $9$ and $4$ .

$x^{\frac{13}{12}} x^{\frac{- 1}{2}}$

Step 2

Multiply $x^{\frac{13}{12}}$ by $x^{\frac{- 1}{2}}$ by adding the exponents.

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Step 2.1

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

$x^{\frac{13}{12} + \frac{- 1}{2}}$

Step 2.2

Move the negative in front of the fraction.

$x^{\frac{13}{12} - \frac{1}{2}}$

Step 2.3

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$x^{\frac{13}{12} - \frac{1}{2} \cdot \frac{6}{6}}$

Step 2.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

Multiply $\frac{1}{2}$ by $\frac{6}{6}$ .

$x^{\frac{13}{12} - \frac{6}{2 \cdot 6}}$

Step 2.4.2

Multiply $2$ by $6$ .

$x^{\frac{13}{12} - \frac{6}{12}}$

Step 2.5

Combine the numerators over the common denominator.

$x^{\frac{13 - 6}{12}}$

Step 2.6

Subtract $6$ from $13$ .

$x^{\frac{7}{12}}$