Pre-Algebra Examples

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

Step 1

Multiply $k^{\frac{2}{3}}$ by $k^{- 1}$ 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.

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

Step 1.2

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

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

Step 1.3

Combine $- 1$ and $\frac{3}{3}$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $- 1$ by $3$ .

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

Step 1.5.2

Subtract $3$ from $2$ .

$\frac{k^{\frac{1}{3}}}{k^{\frac{- 1}{3}}}$

Step 1.6

Move the negative in front of the fraction.

$\frac{k^{\frac{1}{3}}}{k^{- \frac{1}{3}}}$

Step 2

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

$k^{\frac{1}{3}} k^{\frac{1}{3}}$

Step 3

Multiply $k^{\frac{1}{3}}$ by $k^{\frac{1}{3}}$ 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.

$k^{\frac{1}{3} + \frac{1}{3}}$

Step 3.2

Combine the numerators over the common denominator.

$k^{\frac{1 + 1}{3}}$

Step 3.3

Add $1$ and $1$ .

$k^{\frac{2}{3}}$