Evaluate 9^(1/3)*9^(1/6)

$9^{\frac{1}{3}} \cdot 9^{\frac{1}{6}}$

Step 1

Multiply $9^{\frac{1}{3}}$ by $9^{\frac{1}{6}}$ by adding the exponents.

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

$9^{\frac{1}{3} + \frac{1}{6}}$

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

$9^{\frac{1}{3} \cdot \frac{2}{2} + \frac{1}{6}}$

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

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

$9^{\frac{2}{3 \cdot 2} + \frac{1}{6}}$

Multiply $3$ by $2$ .

$9^{\frac{2}{6} + \frac{1}{6}}$

Combine the numerators over the common denominator.

$9^{\frac{2 + 1}{6}}$

Add $2$ and $1$ .

$9^{\frac{3}{6}}$

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3$ .

$9^{\frac{3 (1)}{6}}$

Cancel the common factors.

Factor $3$ out of $6$ .

$9^{\frac{3 \cdot 1}{3 \cdot 2}}$

Cancel the common factor.

$9^{\frac{3 \cdot 1}{3 \cdot 2}}$

Rewrite the expression.

$9^{\frac{1}{2}}$

Step 2

Simplify the expression.

Rewrite $9$ as $3^{2}$ .

${(3^{2})}^{\frac{1}{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$3^{2 (\frac{1}{2})}$

Step 3

Cancel the common factor of $2$ .

Cancel the common factor.

$3^{2 (\frac{1}{2})}$

Rewrite the expression.

$3^{1}$

Step 4

Evaluate the exponent.

$3$