Evaluate each expression. (-2)⁴

Verified step by step guidance

1. Identify the base and the exponent in the expression \((-2)^4\). Here, the base is \(-2\) and the exponent is \(4\).
2. Recall that an exponent indicates how many times to multiply the base by itself. So, \((-2)^4\) means \((-2) \times (-2) \times (-2) \times (-2)\).
3. Multiply the base step-by-step: first multiply the first two factors, then multiply the result by the next factor, and so on.
4. Remember that multiplying two negative numbers results in a positive number, so keep track of the signs carefully during multiplication.
5. Continue multiplying until all four factors are multiplied together to find the final value of \((-2)^4\).

Key Concepts

Exponents and Powers

An exponent indicates how many times a base number is multiplied by itself. For example, in (-2)^4, the base is -2 and the exponent 4 means multiplying -2 by itself four times.

Negative Base with Even Exponent

When a negative number is raised to an even exponent, the result is positive because multiplying an even number of negative factors results in a positive product.

Order of Operations and Parentheses

Parentheses indicate that the negative sign is part of the base. Thus, (-2)^4 means the entire -2 is raised to the fourth power, unlike -2^4, which would mean the negative of 2 raised to the fourth power.