Problem 17 - College Algebra Essentials

Question

Evaluate each exponential expression. $$\frac{2^{8}}{2^{4}}$$

Step-by-Step Solution

Answer

The result of the simplification is 16.

Step 1: Identify the base and the exponent

The base in both terms is 2. The exponent in the numerator is 8 and in the denominator is 4.

Step 2: Apply the division property of exponents

The division property of exponents states that \(a^{m} ÷ a^{n} = a^{m-n}\). So, \(\frac{2^{8}}{2^{4}} = 2^{8-4}\).

Step 3: Subtract the exponents

Subtract the exponent in the denominator from the exponent in the numerator. Hence, \(2^{8-4} = 2^{4}\).

Step 4: Calculate the result

Raising 2 to the power of 4 equals 16. Hence, \(2^{4} = 16\).