Problem 6 - Algebra and Trigonometry

Question

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

Step-by-Step Solution

Answer

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

Step 1: Understand exponential notation

Exponential notation consists of the base, here -2, and the exponent, that's 4. The exponent tells us how many times to multiply the base by itself.

Step 2: Apply the rule of the exponent

The exponent here is an 4, which is an even number. When a negative number, which is our base -2 here, is raised to an even exponent, the result is positive. Therefore, we multiply -2 by itself 4 times: \( (-2) \times (-2) = 4 \), and then multiply the result two more times: \( 4 \times 4 = 16 \).

Step 3: Write down the result

The result of evaluating the exponential expression is thus positive 16.