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Chapter 0: Problem 12

Evaluate each exponential expression. $$2^{-6}$$

Short Answer

Expert verified
The evaluation of the expression \(2^{-6}\) yields \(\frac{1}{64}\).

Step by step solution

01

Understanding Negative Exponents

Any number to the power of a negative exponent can be expressed as one divided by that number to the power of the same positive exponent. This is mathematically expressed as \(a^{-n} = \frac{1}{a^n}\), where a is any real number and n is a positive integer. In this case, \(a = 2\) and \(n = 6\).
02

Evaluating the Exponential Expression

Using the rule for negative exponents, \(2^{-6}\) can be rewritten as \(\frac{1}{2^6}\).
03

Performing the Division

Now, calculate \(2^6\), which is \(64\). Substitute this into the denominator of \(\frac{1}{2^6}\), yielding \(\frac{1}{64}\).

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