Problem 14 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The result is 243

Step 1: Identify the Base and Exponents

Here, the base of both exponential expressions is 3, and the exponents are 3 and 2 respectively. Write it as \(3^{3} \cdot 3^{2}\)

Step 2: Apply the Product of Powers Rule

According to the product of powers rule, \(3^{3} \cdot 3^{2}\) can be written as \(3^{3+2}\)

Step 3: Solve the Exponential Expression

Add the exponents and simplify the expression, we get \(3^{5}\)

Step 4: Compute the Result

Now, calculate the base 3 raised to the power of 5 to get the numerical value. The result is 243