Simplify a^(14/3)*a^(5/6)

$a^{\frac{14}{3}} \cdot a^{\frac{5}{6}}$

Step 1

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

$a^{\frac{14}{3} + \frac{5}{6}}$

Step 2

To write $\frac{14}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$a^{\frac{14}{3} \cdot \frac{2}{2} + \frac{5}{6}}$

Step 3

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

Multiply $\frac{14}{3}$ by $\frac{2}{2}$ .

$a^{\frac{14 \cdot 2}{3 \cdot 2} + \frac{5}{6}}$

Multiply $3$ by $2$ .

$a^{\frac{14 \cdot 2}{6} + \frac{5}{6}}$

Step 4

Combine the numerators over the common denominator.

$a^{\frac{14 \cdot 2 + 5}{6}}$

Step 5

Simplify the numerator.

Multiply $14$ by $2$ .

$a^{\frac{28 + 5}{6}}$

Add $28$ and $5$ .

$a^{\frac{33}{6}}$

Step 6

Cancel the common factor of $33$ and $6$ .

Factor $3$ out of $33$ .

$a^{\frac{3 (11)}{6}}$

Cancel the common factors.

Factor $3$ out of $6$ .

$a^{\frac{3 \cdot 11}{3 \cdot 2}}$

Cancel the common factor.

$a^{\frac{3 \cdot 11}{3 \cdot 2}}$

Rewrite the expression.

$a^{\frac{11}{2}}$