Evaluate the following fractional or decimal expression.
(A) ${(-\frac{1}{2})}^5$

• A. $-\frac{1}{32}$
• B. $-\frac{1}{10}$
• C. $\frac{1}{32}$
• D. $-\frac{1}{25}$

Answer: (A)

Verified step by step guidance

1. Identify the expression to evaluate: \(\left(-\frac{1}{2}\right)^5\).
2. Recall that raising a fraction to a power means raising both the numerator and the denominator to that power: \(\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}\).
3. Apply the exponent to the numerator and denominator separately: \(\left(-1\right)^5\) for the numerator and \$2^5$ for the denominator.
4. Determine the sign of the result by considering the exponent on the negative number: since 5 is an odd number, \(\left(-1\right)^5 = -1\).
5. Combine the results to write the final expression as \(-\frac{1^5}{2^5} = -\frac{1}{32}\).