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Chapter 5: Problem 135

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \((-2)^{4}=2^{-4}\)

Short Answer

Expert verified
The statement \((-2)^4=2^{-4}\) is false. A true statement would be \((-2)^4=\(\frac{1}{2^{-4}}\).

Step by step solution

01

Evaluate the Left Side

Start by evaluating the expression on the left side of the equation \((-2)^{4}\). This means \(-2\) times \(-2\) times \(-2\) times \(-2\), which gives 16.
02

Evaluate the Right Side

Next, evaluate the expression on the right side. The expression \(2^{-4}\) means 1 divided by \(2^{4}\), or \(\frac{1}{2*2*2*2}\), which gives \(\frac{1}{16}\).
03

Compare the Results

The results are not the same, the left side equates to 16 while the right side equates to \(\frac{1}{16}\), so the given statement is false.
04

Make the Statement True

To make the statement true, you can change it to \((-2)^4=\(\frac{1}{2^{-4}}\), because both sides of the equation will equal 16.

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