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Chapter 0: Problem 19

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

Short Answer

Expert verified
The result of the expression \(3^{-3} \cdot 3\) is approximately 0.11.

Step by step solution

01

Calculate the Exponential Part

First, determine the value of \(3^{-3}\). The negative exponent indicates that we should take the reciprocal of the base, so \(3^{-3} = 1/3^3\). Then calculate \(3^3\), which equals 27. Thus, \(3^{-3} = 1/27 = 0.037037\
02

Perform the Multiplication

Multiply \(3^{-3}\) by 3. Hence, \(3^{-3} * 3 = 0.037037 * 3 = 0.111111\).
03

Approximate the Result

Lastly, approximate the result. The number 0.111111 can be approximated to 0.11 to keep two decimal places.

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