Question: Evaluate the expression \(-81^{3/4}\), if possible. Select the correct choice below and fill in…

Evaluate the expression \(-81^{3/4}\), if possible.

Select the correct choice below and fill in any answer boxes in your choice.

A. \(-81^{3/4} = \boxed{\phantom{0}}\)

B. The solution is not a real number.

Solution

The problem is to evaluate the expression \( -81^{3/4} \). First, consider the expression inside the power: \[ 81^{3/4} \] 81 can be rewritten as \( 3^4 \), so: \[ (3^4)^{3/4} \] Applying the property of exponents \((a^m)^n = a^{m \times n}\), we get: \[ 3^{4 \times \frac{3}{4}} \] Simplify the exponent: \[ 3^3 \] Calculate \(3^3\): \[ 3^3 = 27 \] Now return to the original expression and compute the negative: \[ -81^{3/4} = -27 \] Thus, the solution is: \[ -27 \]