Simplify a^(10/3)*a^(1/6)

$a^{\frac{10}{3}} \cdot a^{\frac{1}{6}}$

Step 1

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

$a^{\frac{10}{3} + \frac{1}{6}}$

Step 2

To write $\frac{10}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$a^{\frac{10}{3} \cdot \frac{2}{2} + \frac{1}{6}}$

Step 3

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

Multiply $\frac{10}{3}$ by $\frac{2}{2}$ .

$a^{\frac{10 \cdot 2}{3 \cdot 2} + \frac{1}{6}}$

Multiply $3$ by $2$ .

$a^{\frac{10 \cdot 2}{6} + \frac{1}{6}}$

Step 4

Combine the numerators over the common denominator.

$a^{\frac{10 \cdot 2 + 1}{6}}$

Step 5

Simplify the numerator.

Multiply $10$ by $2$ .

$a^{\frac{20 + 1}{6}}$

Add $20$ and $1$ .

$a^{\frac{21}{6}}$

Step 6

Cancel the common factor of $21$ and $6$ .

Factor $3$ out of $21$ .

$a^{\frac{3 (7)}{6}}$

Cancel the common factors.

Factor $3$ out of $6$ .

$a^{\frac{3 \cdot 7}{3 \cdot 2}}$

Cancel the common factor.

$a^{\frac{3 \cdot 7}{3 \cdot 2}}$

Rewrite the expression.

$a^{\frac{7}{2}}$