Simplify a^(5/6)*a^(-1/2)

$a^{\frac{5}{6}} \cdot a^{- \frac{1}{2}}$

Step 1

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

$a^{\frac{5}{6} - \frac{1}{2}}$

Step 2

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

$a^{\frac{5}{6} - \frac{1}{2} \cdot \frac{3}{3}}$

Step 3

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

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

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

Multiply $2$ by $3$ .

$a^{\frac{5}{6} - \frac{3}{6}}$

Step 4

Combine the numerators over the common denominator.

$a^{\frac{5 - 3}{6}}$

Step 5

Subtract $3$ from $5$ .

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

Step 6

Cancel the common factor of $2$ and $6$ .

Factor $2$ out of $2$ .

$a^{\frac{2 (1)}{6}}$

Cancel the common factors.

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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