Problem 53 - College Algebra Essentials

Question

Simplify each exponential expression. $$\frac{14 b^{7}}{7 b^{14}}$$

Step-by-Step Solution

Answer

The simplified form of the expression \(\frac{14 b^{7}}{7 b^{14}}\) is \(2 / b^{7}\).

Step 1: Simplify the Numerical Coefficients

Divide the coefficient 14 in the numerator by the coefficient 7 in the denominator. We get \(14 / 7 = 2\).

Step 2: Apply the Quotient Rule for Exponents

Subtract the exponent of \(b\) in the denominator from the exponent of \(b\) in the numerator. We then have \(b^{7} / b^{14} = b^{7-14}\). This simplifies to \(b^{-7}\). This represents an inverse, and is typically written as \(1/b^{7}\).

Step 3: Combine the Results

Combine the results from step 1 and step 2 to get the simplified expression. The simplified form of the expression is \(2 / b^{7}\).