Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 7 - Exponents and Exponential Functions - 7-1 Zero and Negative Exponents - Lesson Check - Page 417: 6



Work Step by Step

We want to simplify the expression: $2a^{-4}b^0$ The zero as an exponent rule states that for every nonzero number $a$, $a^0=1$. This expression contains $b^0$, which must be equal to $1$. The identity property of multiplication states that the product of any real number and $1$ is the original number. Therefore, we can reduce the expression to $2a^{-4}$ The negative exponent rule states that for every nonzero number $a$ and integer $n$, $a^{-n}=\frac{1}{a^n}$. We can use this to rewrite the expression as $\frac{2}{a^4}$. Now, we can plug in the value for $a$: $\frac{2}{2^4}$ The order of operations states that first we perform operations inside grouping symbols, such as parentheses, brackets, and fraction bars. Then, we simplify powers. Then, we multiply and divide from left to right. We follow the order of operations to simplify: First, we simplify below the fraction bar: $\frac{2}{16}$ Finally, we divide: $\frac{1}{8}=0.125$
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