Evaluate the following Expression.
${(-4)}^4$

• A. $16$
• B. $-256$
• C. $-16$
• D. $256$

Answer: (D)

Verified step by step guidance

1. Identify the base and the exponent in the given exponential expression. Since the problem mentions negative bases, pay attention to whether the base is enclosed in parentheses, as this affects the sign of the result.
2. Recall the rule for exponents with negative bases: if the exponent is an even integer, the result will be positive; if the exponent is an odd integer, the result will be negative. This is because multiplying a negative number an even number of times results in a positive product, while an odd number of times keeps it negative.
3. Rewrite the expression clearly, for example, if the expression is \((-a)^n\), note that the negative sign is part of the base. If the expression is \(-a^n\), the negative sign is not part of the base and applies after exponentiation.
4. Calculate the exponentiation by multiplying the base by itself the number of times indicated by the exponent, keeping track of the sign according to the parity of the exponent.
5. Simplify the expression fully, combining any like terms or constants, and write the final expression with the correct sign based on the previous steps.