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Chapter 1: Problem 26

Evaluate. $$(-2)^{4}$$

Short Answer

Expert verified
So, to evaluate \((-2)^4\), we simply need to multiply the base, -2, times itself four times: \((-2) \times (-2) \times (-2) \times (-2)\). This results in the final answer of \(\boxed{16}\).

Step by step solution

01

Understand the meaning of the exponent

In this expression, \((-2)^4\), the exponent is 4. An exponent is a shorthand way to represent repeated multiplication. So, we need to multiply the base, -2, times itself four times.
02

Set up the expression

We can rewrite the expression as follows: \[ (-2)^4 = (-2) \times (-2) \times (-2) \times (-2) \]
03

Multiply the numbers

Now we will simply multiply the numbers: \[ (-2) \times (-2) = 4 \] And then, we multiply the result by the next -2: \[ 4 \times (-2) = -8 \] Lastly, we multiply the result by the final -2: \[ -8 \times (-2) = 16 \]
04

Write the final answer

So, \((-2)^4\) equals 16. The answer is 16.

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