Evaluate (-81)^(1/2)

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

Step 1

Simplify the expression.

Rewrite $- 81$ as ${(9 i)}^{2}$ .

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

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

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

Step 2

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

${(9 i)}^{1}$

Step 3

Simplify.

$9 i$