Problem 13 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The evaluation of the expression \(2^{2} \cdot 2^{3}\) is 32.

Step 1: Identify the Base and Exponents

The expression presented is \(2^{2} \cdot 2^{3}\). Here, the base is 2 and the exponents are 2 and 3, which applies to the first and second terms, respectively.

Step 2: Apply the Property of Exponents

By the property of exponents, when multiplying expressions with the same base, the exponents are added. So, the expression \(2^{2} \cdot 2^{3}\) becomes \(2^{2+3}\).

Step 3: Evaluate the New Expression

Now add the exponents: \(2^{2+3} = 2^{5}\).

Step 4: Calculate the Final Answer

Finally, raise the base 2 to the power of 5: \(2^{5} = 32\).