Problem 18 - College Algebra Essentials

Question

Evaluate each exponential expression. $$\frac{3^{8}}{3^{4}}$$

Step-by-Step Solution

Answer

The solution to the given exponential expression \(\frac{3^{8}}{3^{4}}\) is 81.

Step 1: Identify the Base and Exponents

Here, base=3 and there are two exponents: 8 and 4. The given expression is \(3^{8}/3^{4}\).

Step 2: Apply the Quotient Rule of Exponents

When dividing expressions with the same base, subtract the exponent in the denominator from the exponent in the numerator. By quotient rule, \(3^{8}/3^{4}\) simplifies to \(3^{8-4}\).

Step 3: Simplify the Expression

Subtract the exponents: \(3^{8-4}\) becomes \(3^{4}\).

Step 4: Evaluate the Exponential Expression

The expression \(3^{4}\) equals 81. So, the final solution is 81.