Evaluate each expression. (-2)⁶

Verified step by step guidance

1. Identify the base and the exponent in the expression \((-2)^6\). Here, the base is \(-2\) and the exponent is \(6\).
2. Recall that an exponent indicates how many times the base is multiplied by itself. So, \((-2)^6\) means \((-2) \times (-2) \times (-2) \times (-2) \times (-2) \times (-2)\).
3. Since the exponent is even, multiplying a negative number an even number of times results in a positive number. This is because each pair of negative factors multiplies to a positive.
4. Calculate the value of \$2^6$ by multiplying \(2\) by itself six times: \(2 \times 2 \times 2 \times 2 \times 2 \times 2\).
5. Combine the sign consideration from step 3 with the magnitude from step 4 to determine the final value of \((-2)^6\).

Key Concepts

Exponents and Powers

An exponent indicates how many times a base number is multiplied by itself. For example, in (-2)^6, the base is -2 and the exponent 6 means multiplying -2 by itself six 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)^6 means the entire -2 is raised to the 6th power, unlike -2^6, which would mean the negative of 2 raised to the 6th power.