Question

Evaluate the expression. $$\left(\frac{1}{2}\right)^{3}$$

Short answer

The result of evaluating the expression \(\left(\frac{1}{2}\right)^{3}\) is \(\frac{1}{8}\).

Step-by-step solution

Process the Exponential Expression

An exponential expression means the base, which is \(\frac{1}{2}\) in our case, should be multiplied by itself for a number of times equal to the exponent, which is 3 here. So, computing the expression \(\left(\frac{1}{2}\right)^{3}\) involves multiplying \(\frac{1}{2}\) by itself twice.

Perform the Multiplication

Performing the multiplication, we have \(\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}\). When multiplying fractions, we simply multiply the numerators together to get the new numerator and do the same for the denominators.