Basic Math Examples

$a^{\frac{1}{2}} \div a^{\frac{1}{3}}$

Step 1

Rewrite the division as a fraction.

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

Step 2

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

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

Step 3

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

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

Step 3.2

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3.3

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

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

Step 3.4.2

Multiply $2$ by $3$ .

$a^{\frac{3}{6} - \frac{1}{3} \cdot \frac{2}{2}}$

Step 3.4.3

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$a^{\frac{3}{6} - \frac{2}{3 \cdot 2}}$

Step 3.4.4

Multiply $3$ by $2$ .

$a^{\frac{3}{6} - \frac{2}{6}}$

Step 3.5

Combine the numerators over the common denominator.

$a^{\frac{3 - 2}{6}}$

Step 3.6

Subtract $2$ from $3$ .

$a^{\frac{1}{6}}$