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Chapter 0: Problem 4

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

Short Answer

Expert verified
The value of \(-2^4\) is 16.

Step by step solution

01

Understand the Base and the Exponent

In our expression \(-2^4\), the base is \(-2\), and the exponent is \(4\). This means we have to multiply the base, \(-2\), by itself \(4-1=3\) more times (since the first \(-2\) is already counted). Remember, an exponent of 4 means that we have to use the base number 4 times in a multiplication.
02

Perform the operation

We do the multiplication as follows: \[(-2) \times (-2) \times (-2) \times (-2)\] A negative times a negative gives a positive, so here we will have four pairs of \(-2\) times \(-2\), which yields a positive result each time. That is: \[(4) \times (4)\] This equals 16.

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