Evaluate (81^3)^(1/6)

${(81^{3})}^{\frac{1}{6}}$

Step 1

Simplify the expression.

Multiply the exponents in ${(81^{3})}^{\frac{1}{6}}$ .

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

$81^{3 (\frac{1}{6})}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$81^{3 \frac{1}{3 (2)}}$

Cancel the common factor.

$81^{3 \frac{1}{3 \cdot 2}}$

Rewrite the expression.

$81^{\frac{1}{2}}$

Rewrite $81$ as $9^{2}$ .

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

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

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

Step 2

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$9^{1}$

Step 3

Evaluate the exponent.

$9$