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 - Page 224: 118



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: $=\dfrac{6(10^{-3}) \cdot 6(10^{2})}{4(10^{-5})\cdot 3(10^{1})} \\=\dfrac{6\cdot 6(10^{-3+2})}{4.\cdot 3(10^{-5+1})} \\=\dfrac{36(10^{-1})}{12(10^{-4})}$ Divide $36$ and $12$ together and divide the powers of 10 together to obtain: $=\dfrac{36}{12} \cdot \dfrac{10^{-1}}{10^{-4}} \\=3 \cdot 10^{-1-(-4)} \\=3 \cdot 10^{-1+4} \\=3 \cdot 10^3 \\=3,000$
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