Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Section P.2 - Exponents and Scientific Notation - Exercise Set - Page 31: 126


The quotient rule for exponents is that when dividing two powers with the same base, keep the same base and subtract the powers.

Work Step by Step

For $\frac{5^{8}}{5^{2}}$, keep 5 as the base and subtract the denominator's exponent (2) from the numerator's (8): $5^{8-2} = 5^{6} = 15625$. You can also view this as "cancelling out": there are eight 5's on top and two on the bottom, so two 5's can be cancelled out from both the top and the bottom, leaving us with six 5's on top. This is helpful if the exponent in the denominator is larger than that in the numerator (e.g. $\frac{5^{2}}{5^{8}}$). The $5^{2}$ on top cancels out to leave a 1, and six 5's are left on the bottom, leaving us with $\frac{1}{5^{6}} = \frac{1}{15625}$.
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