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Chapter 0: Problem 19

Evaluate each exponential expression. $$ 3^{-3} \cdot 3 $$

Short Answer

Expert verified
The evaluated exponential expression is \(\frac{1}{9}\).

Step by step solution

01

Evaluate Exponential part

Exponentiation is the action of raising a number to a power. Here, 3 is raised to the power of -3. The negative exponent means that we take the reciprocal of 3 to the power of 3 which is \(3^{-3} = \frac{1}{3^3}\) or \(\frac{1}{27}\).
02

Multiply with 3

Next, multiply the result from the previous step with 3. We have \(\frac{1}{27} \cdot 3 = \frac{3}{27}\).
03

Simplify the expression

Finally, simplify \(\frac{3}{27}\) yielding \(\frac{1}{9}\).

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Most popular questions from this chapter

Describe the kinds of numbers that have rational fifth roots.

In one short sentence, five words or less, explain what $$ \frac{\frac{1}{x}+\frac{1}{x^{2}}+\frac{1}{x^{3}}}{\frac{1}{x^{4}}+\frac{1}{x^{5}}+\frac{1}{x^{6}}} $$ does to each number \(x\).

Explain how to factor the difference of two squares. Provide an example with your explanation.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Some whole numbers are not integers.

Will help you prepare for the material covered in the next section. A. Use a calculator to approximate \(\sqrt{300}\) to two decimal places. B. Use a calculator to approximate \(10 \sqrt{3}\) to two decimal places. C. Based on your answers to parts (a) and (b), what can you conclude?
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