Basic Math Examples

$a^{\frac{5}{6}} \cdot a^{\frac{2}{3}}$

Step 1

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

$a^{\frac{5}{6} + \frac{2}{3}}$

Step 2

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

$a^{\frac{5}{6} + \frac{2}{3} \cdot \frac{2}{2}}$

Step 3

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

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Step 3.1

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

$a^{\frac{5}{6} + \frac{2 \cdot 2}{3 \cdot 2}}$

Step 3.2

Multiply $3$ by $2$ .

$a^{\frac{5}{6} + \frac{2 \cdot 2}{6}}$

Step 4

Combine the numerators over the common denominator.

$a^{\frac{5 + 2 \cdot 2}{6}}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $2$ by $2$ .

$a^{\frac{5 + 4}{6}}$

Step 5.2

Add $5$ and $4$ .

$a^{\frac{9}{6}}$

Step 6

Cancel the common factor of $9$ and $6$ .

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Step 6.1

Factor $3$ out of $9$ .

$a^{\frac{3 (3)}{6}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $3$ out of $6$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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