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Chapter 5: Problem 30

Use properties of exponents to simplify each expression. First express the answer in exponential form. Then evaluate the expression. \(\frac{3^{4}}{3^{7}}\)

Short Answer

Expert verified
\(\frac{1}{27}\)

Step by step solution

01

Applying Division Property of Exponents

The key here is that we have an expression that can be simplified using the division property of exponents. According to this rule, when we divide like bases, we subtract the exponents. This gives us \(3^{4-7}\).
02

Subtract the Exponents

Now, proceed and subtract the exponents of the expression obtained in Step 1. The new expression is \(3^{-3}\).
03

Understand the Negative Exponent

A negative exponent represents the reciprocal of the base to the positive exponent. So, \(3^{-3}\) is same as \(\frac{1}{3^{3}}\).
04

Evaluate The Expression

Lastly, evaluate the expression \(\frac{1}{3^{3}}\), which simplifies to \(\frac{1}{27}\).

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Most popular questions from this chapter

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(5,15,45,135, \ldots\)

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{6}\), when \(a_{1}=-2, r=-3\).

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

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{40}\), when \(a_{1}=6, r=-1\).

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(7,-7,-21,-35, \ldots\)
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