Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 5 - Exponents and Polynomials - 5.6 - Integral Exponents and Scientific Notation - Problem Set 5.6: 117

Answer

$0.000007$

Work Step by Step

RECALL: (i) Scientific notation has the form $a(10^n)$, where $1 \le a \lt 10$ and where $n$ is an integer. (ii) $\frac{a^{m}}{a^{n}}=a^{m-n}$ (iii) $a^{m}a^{n}=a^{m+n}$ Write each number in scientific notation to obtain: $=\dfrac{8(10^{-4}) \cdot 7(10^{-2})}{2(10^{4})\cdot 4(10^{-4})} \\=\dfrac{8\cdot 7(10^{-4+(-2)})}{2.\cdot 4(10^{4+(-4)})} \\=\dfrac{56(10^{-6})}{8(10^{0})} \\=\dfrac{56(10^{-6})}{8\cdot 1} \\=\dfrac{56(10^{-6})}{8} $ Divide $56$ and $7$ together to obtain: $=\dfrac{56}{8} \cdot 10^{-6} \\=7 \cdot 10^{-6} \\=0.000007$
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