Finite Math Examples

$\frac{10 x^{2}}{x^{\frac{1}{3}}}$

Step 1

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

$10 x^{2} x^{- \frac{1}{3}}$

Step 2

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

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Step 2.1

Move $x^{- \frac{1}{3}}$ .

$10 (x^{- \frac{1}{3}} x^{2})$

Step 2.2

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

$10 x^{- \frac{1}{3} + 2}$

Step 2.3

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

$10 x^{- \frac{1}{3} + 2 \cdot \frac{3}{3}}$

Step 2.4

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

$10 x^{- \frac{1}{3} + \frac{2 \cdot 3}{3}}$

Step 2.5

Combine the numerators over the common denominator.

$10 x^{\frac{- 1 + 2 \cdot 3}{3}}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $2$ by $3$ .

$10 x^{\frac{- 1 + 6}{3}}$

Step 2.6.2

Add $- 1$ and $6$ .

$10 x^{\frac{5}{3}}$