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Chapter 2: Problem 2

True or False: \(6^{0}-4^{0}=(6-4)^{0}\)

Short Answer

Expert verified
False. The left side is \(6^{0} - 4^{0} = 1 - 1 = 0\), whereas the right side is \((6 - 4)^{0} = 2^{0} = 1\). Since 0 is not equal to 1, the statement is false.

Step by step solution

01

Evaluate Left Side of the Equation

Calculate \(6^{0} - 4^{0}\) by remembering that any non-zero number to the power of 0 is equal to 1: \[6^{0} = 1\] \[4^{0} = 1\] \[6^{0} - 4^{0} = 1 - 1 = 0\]
02

Evaluate Right Side of the Equation

Calculate \((6 - 4)^{0}\) by first evaluating the expression in the parentheses and then raising it to the power of 0: \[(6 - 4) = 2\] \[(6 - 4)^{0} = 2^{0} = 1\]
03

Compare the Results

Now that we have evaluated both sides of the equation, we can compare the results: \[6^{0} - 4^{0} = 0\] \[(6 - 4)^{0} = 1\] Since 0 is not equal to 1, the statement given as \(6^{0} - 4^{0} = (6 - 4)^{0}\) is False.

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