Problem 20 - Algebra and Trigonometry

Question

Evaluate each exponential expression. $$ 2^{-3} \cdot 2 $$

Step-by-Step Solution

Answer

The answer to the expression \(2^{-3} \cdot 2\) is \(1/4\).

Step 1: Evaluate the Exponential Part

Start by calculating \(2^{-3}\). A negative exponent means we take the reciprocal of the base, so \(2^{-3}=1/2^3\). Now simplify \(2^3\) which gives us 8, so \(2^{-3}=1/8\).

Step 2: Multiply by 2

Now, replace \(2^{-3}\) with \(1/8\) in the original problem, which gives us \(1/8 \cdot 2\). Multiply these numbers together to find the solution.

Step 3: Calculate the Answer

Multiplying \(1/8\) and 2 gives a result of \(1/4\). This is the solution.