Calculate (-3)^4: Evaluating Negative Numbers Raised to Powers

To solve the problem $(-3)^4$, we'll perform the following computations step-by-step:

• Step 1: Consider $(-3) \times (-3)$. This equals $9$ because multiplying two negative numbers results in a positive number.
• Step 2: Use the result from Step 1 and multiply it by $(-3)$: $9 \times (-3) = -27$.
• Step 3: Finally, multiply the result from Step 2 by $(-3)$: $-27 \times (-3) = 81$.

The properties of exponents ensure that $(-3)^4$ results in a positive number because the exponent is even.

Therefore, the solution to the problem is $\textbf{81}$. The correct answer corresponds to choice 3.