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Chapter 5: Problem 24

Use the zero and negative exponent rules to simplify each expression. \(2^{-6}\)

Short Answer

Expert verified
The expression \(2^{-6}\) simplifies to \(1/64\).

Step by step solution

01

Understand the Negative Exponent Rule

We need to recall that for any non-zero number \(a\), the negative exponent property, \(a^{-n} = 1/a^n\), is valid. That is, a negative exponent indicates that the base number is to be divided into 1, not multiplied.
02

Apply the Negative Exponent Rule

Now that we have the expression \(2^{-6}\), we can apply this rule to it. So it becomes \(1/2^6\).
03

Simplify the Expression

Now we just need to calculate the value of \(2^6\) and then divide 1 by that value. \(2^6 = 64\), therefore the expression simplifies to \(1/64\) after calculation.

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Most popular questions from this chapter

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{30}\), when \(a_{1}=8000, r=-\frac{1}{2}\).

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=3, r=-2\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=-2, r=-3\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(2,6,10,14, \ldots\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=1000, r=1\)
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