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

• 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 base and the exponent in the given exponential expression. Since the problem involves negative bases, pay close attention to whether the negative sign is inside the parentheses or not.
2. Recall the rule that when a negative number is raised to an even exponent, the result is positive, and when raised to an odd exponent, the result is negative. This is because multiplying an even number of negative factors results in a positive product, while an odd number results in a negative product.
3. Rewrite the expression clearly, for example, if the expression is \((-a)^n\), note that the negative sign is part of the base, but if it is \(-a^n\), the negative sign is separate and only the \(a\) is raised to the power \(n\).
4. Calculate the absolute value of the base raised to the exponent, ignoring the negative sign for now. This means computing \(a^n\) where \(a\) is the positive value of the base.
5. Apply the sign determined in step 2 to the result from step 4. If the exponent is even, the result is positive; if odd, the result is negative. This gives you the final value of the exponential expression with a negative base.