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Chapter 0: Problem 53

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

Short Answer

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

Step by step solution

01

Simplify the Numerical Coefficients

Divide the coefficient 14 in the numerator by the coefficient 7 in the denominator. We get \(14 / 7 = 2\).
02

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 \(1/b^{7}\).
03

Combine the Results

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

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