Problem 17 - Algebra and Trigonometry

Question

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

Step-by-Step Solution

Answer

The solution to the expression \( \frac{2^{8}}{2^{4}} \) is 16.

Step 1: Identify the expression

We have the expression \( \frac{2^{8}}{2^{4}} \). In this expression, notice that 2 is the base for both exponents.

Step 2: Apply the rule of exponents

According to the rule for dividing powers with the same base (a^(m)/a^(n) = a^(m-n)), we can subtract the exponent in the denominator from the exponent in the numerator. Therefore, this expression becomes \(2^{8-4}\)

Step 3: Calculate the exponent

Now, we execute the subtraction operation in the exponent to get \(2^{4}\)

Step 4: Solve the exponential expression

Now, evaluate \(2^{4}\). Two raised to the power of four equals to 16.