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Chapter 5: Problem 134

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \(5^{-2}>2^{-5}\)

Short Answer

Expert verified
The statement \(5^{-2}>2^{-5}\) is true.

Step by step solution

01

Evaluate Left-Hand Side

Calculate the value for \(5^{-2}\). A negative exponent means that we take the reciprocal of the base. So, \(5^{-2} = 1/(5^{2}) = 1/25 = 0.04.
02

Evaluate Right-Hand Side

Calculate the value for \(2^{-5}\). Similarly, we take the reciprocal of \(2^{5}\). Thus, \(2^{-5} = 1/(2^{5}) = 1/32 = 0.03125.
03

Compare the Results

Comparison of the calculated values. The inequality \(0.04 > 0.03125\) holds true. Thus, the original statement is correct.

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Most popular questions from this chapter

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, \(r\). \(a_{1}=2, r=0.1\)

Use the appropriate formula shown above to find \(2+4+6+8+\cdots+200\), the sum of the first 100 positive even integers.

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{8}\), when \(a_{1}=40,000, r=0.1\).

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. A sequence that is not arithmetic must be geometric.
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