## Intermediate Algebra for College Students (7th Edition)

$\dfrac{1}{10^{14}}$
Use the rule $\dfrac{a^m}{a^n} = a^{m-n}, a\ne0$ to obtain: $=100^{\frac{3}{4}-\frac{31}{4}} \\=100^{-\frac{28}{4}} \\=100^{-7}$ Write 100 as $10^2$ to obtain: $=(10^2)^{-7}$ Use the rule $(a^m)^n=a^{mn}$ to tobtain: $=10^{-14}$ Use the rule $a^{-m} = \dfrac{1}{a^m}$ to obtain: $=\dfrac{1}{10^{14}}$