Finite Math Examples

$\frac{w^{\frac{4}{3}} w^{\frac{2}{3}}}{w^{\frac{1}{3}}}$

Step 1

Multiply $w^{\frac{4}{3}}$ by $w^{\frac{2}{3}}$ 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.

$\frac{w^{\frac{4}{3} + \frac{2}{3}}}{w^{\frac{1}{3}}}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{w^{\frac{4 + 2}{3}}}{w^{\frac{1}{3}}}$

Step 1.3

Add $4$ and $2$ .

$\frac{w^{\frac{6}{3}}}{w^{\frac{1}{3}}}$

Step 1.4

Divide $6$ by $3$ .

$\frac{w^{2}}{w^{\frac{1}{3}}}$

Step 2

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

$w^{2} w^{- \frac{1}{3}}$

Step 3

Multiply $w^{2}$ by $w^{- \frac{1}{3}}$ by adding the exponents.

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Step 3.1

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

$w^{2 - \frac{1}{3}}$

Step 3.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$w^{2 \cdot \frac{3}{3} - \frac{1}{3}}$

Step 3.3

Combine $2$ and $\frac{3}{3}$ .

$w^{\frac{2 \cdot 3}{3} - \frac{1}{3}}$

Step 3.4

Combine the numerators over the common denominator.

$w^{\frac{2 \cdot 3 - 1}{3}}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $2$ by $3$ .

$w^{\frac{6 - 1}{3}}$

Step 3.5.2

Subtract $1$ from $6$ .

$w^{\frac{5}{3}}$