Question: Evaluate the expression, if possible. $$81^{1/4}$$ Select the correct choice below and, if…

Evaluate the expression, if possible.

$$81^{1/4}$$

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. $$81^{1/4} = \boxed{\phantom{0}}$$

B. The solution is not a real number.

Solution

To evaluate the expression \( 81^{1/4} \), we need to find the fourth root of 81. 81 can be written as \( 3^4 \). So, \( 81^{1/4} = (3^4)^{1/4} \). Using the exponentiation rule \((a^m)^n = a^{m \cdot n}\), we get: \[ (3^4)^{1/4} = 3^{4 \cdot \frac{1}{4}} \] \[ 3^{4 \cdot \frac{1}{4}} = 3^1 \] \[ 3^1 = 3 \] Therefore, the value of \( 81^{1/4} \) is 3.