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Chapter 5: Problem 22

Use the zero and negative exponent rules to simplify each expression. \(2^{-3}\)

Short Answer

Expert verified
The simplified form of the expression \(2^{-3}\) is \(\frac{1}{8}\).

Step by step solution

01

Identify the base and the negative exponent

The base in this case is 2, and the exponent is -3. The expression is in the form \(2^{-3}\).
02

Apply the negative exponent rule

According to the rule of negative exponents, we know that \(a^{-n} = 1/a^n\). So, the expression \(2^{-3}\) can be reshaped to fit this formula. The result is \(\frac{1}{2^3}\).
03

Simplify

Now, simply calculate \(2^3 = 2*2*2 = 8\). Replace \(2^3\) in the denominator with 8. The final simplified form of the expression is \(\frac{1}{8}\).

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Most popular questions from this chapter

Enough curiosities involving the Fibonacci sequence exist to warrant a flourishing Fibonacci Association. It publishes a quarterly journal. Do some research on the Fibonacci sequence by consulting the research department of your library or the Internet, and find one property that interests you. After doing this research, get together with your group to share these intriguing properties.

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=-\frac{1}{8}, r=-2\)

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

The bar graph shows changes in the percentage of college graduates for Americans ages 25 and older from 1990 to 2010. Exercises 125-126 involve developing arithmetic sequences that model the data. In \(1990,24.4 \%\) of American men ages 25 and older had graduated from college. On average, this percentage has increased by approximately \(0.3\) each year. a. Write a formula for the \(n\)th term of the arithmetic sequence that models the percentage of American men ages 25 and older who had graduated from college \(n\) years after \(1989 .\) b. Use the model from part (a) to project the percentage of American men ages 25 and older who will be college graduates by \(2019 .\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If a sequence is geometric, we can write as many terms as we want by repeatedly multiplying by the common ratio.
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