Problem 13 - Algebra and Trigonometry

Question

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

Step-by-Step Solution

Answer

The result is 32.

Step 1: Identify the Base

The base of the exponents in this case is 2.

Step 2: Apply the Product of Powers Rule

According to the Product of Powers Rule, if we multiply 2 with the same base, we can add the exponents. So, \(2^{2} \cdot 2^{3}\) can become \(2^{2+3}\).

Step 3: Solve for the Exponent

The exponent is now \(2+3\), which equals 5, so the expression simplifies to \(2^{5}\).

Step 4: Evaluate the Power

Lastly, we calculate the power of 2, which is \(2^{5} = 32\).