Question

what is the value of the exponential expression below?
$64^{\frac{1}{2}}$
a. 8
b. 32
c. 16
d. 4

Explanation:

Step1: Recall the exponent rule

The rule for a fractional exponent \( a^{\frac{1}{n}} \) is that it represents the \( n \)-th root of \( a \), i.e., \( a^{\frac{1}{n}}=\sqrt[n]{a} \). For \( 64^{\frac{1}{2}} \), this means we need to find the square root of 64.

Step2: Calculate the square root

We know that \( 8\times8 = 64 \), so \( \sqrt{64}=8 \). Therefore, \( 64^{\frac{1}{2}} = 8 \).

Answer:

A. 8