Problem 19 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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\

Step 2: Perform the Multiplication

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

Step 3: Approximate the Result

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