Evaluate 3^(9^(2^-1))

$3^{9^{2^{- 1}}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Simplify the expression.

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

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

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

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

Step 3

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$3^{3^{1}}$

Step 4

Evaluate the exponent.

$3^{3}$

Step 5

Raise $3$ to the power of $3$ .

$27$