Problem 21 - College Algebra Essentials

Question

Evaluate each exponential expression. $$\frac{2^{3}}{2^{7}}$$

Step-by-Step Solution

Answer

The simplified form of \(\frac{2^{3}}{2^{7}}\) is \(\frac{1}{2^{4}}\)

Step 1: Writing the expression

The given expression is \(\frac{2^{3}}{2^{7}}\)

Step 2: Applying the properties of exponents

When dividing expressions with same base, subtract the exponent of the denominator from the exponent of the numerator. The equation becomes \(2^{3-7}\)

Step 3: Solving the mathematical expression

Subtract the exponents, which gives \(2^{-4}\). In maths, when an exponent is negative, it means the base is on the wrong side of the fraction line, so flip the base to the other side. The final simplified result is \(\frac{1}{2^{4}}\)