Problem 19 - Algebra and Trigonometry

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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 \(\frac{1}{27}\).

Step 2: Multiply with 3

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

Step 3: Simplify the expression

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