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Chapter 5: Problem 2

Use properties of exponents to simplify each expression. First express the answer in exponential form. Then evaluate the expression. \(3^{3} \cdot 3^{2}\)

Short Answer

Expert verified
The simplified expression is \(3^{5}\), which is 243 when evaluated.

Step by step solution

01

Identify the base and the exponents

The base is 3 and the exponents are 3 and 2. The expression is written as \(3^{3} \cdot 3^{2}\).
02

Apply the exponent addition rule

When multiplying expressions with the same base, add the exponents. So add the exponents 3 and 2. This gives you \(3^{3+2}\).
03

Simplify the exponent

Now, simplify the exponent. Adding the numbers 3 and 2 equals 5. So the expression simplified is \(3^{5}\).
04

Evaluate the expression

Finally, evaluate the expression \(3^{5}\). This gives you 243.

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Most popular questions from this chapter

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(3,8,13,18, \ldots\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(\sqrt{3}, 3,3 \sqrt{3}, 9, \ldots\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(-9,-5,-1,3, \ldots\)

Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for \(a_{n}\) to find \(a_{7}\), the seventh term of the sequence. \(0.0004,-0.004,0.04,-0.4, \ldots\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. There's no end to the number of geometric sequences that I can generate whose first term is 5 if I pick nonzero numbers \(r\) and multiply 5 by each value of \(r\) repeatedly.
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