Problem 4 - College Algebra Essentials

Question

Evaluate each exponential expression. $$(-2)^{4}$$

Step-by-Step Solution

Answer

The result of evaluating the expression \(-2^{4}\) is 16.

Step 1: Understanding the Exponent

Recognize that the number -2 is being raised to the fourth power, which means -2 is multiplied by itself four times.

Step 2: Evaluate the Power

Begin by understanding that \((-2)^{4}\) means \(-2\) multiplied by itself 4 times. This can be written as \((-2) \times (-2) \times (-2) \times (-2)\).

Step 3: Multiply the Numbers

Now, just multiply -2 by itself four times. From multiplication rules, we knows that the multiplication of two negatives numbers yields a positive result. Hence, multiply first two \(-2\), get \((-2) \times (-2) = 4\). Again multiply \(4\) with next \(-2\) get \(4 \times (-2) = -8\). Lastly, multiply \(-8\) with last \(-2\), we get \(-8 \times (-2) = 16\).