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Perform the indicated operations using the laws of exponents. Express the result using a single nonnegative exponent on 10. 10-2. 10-7-4 109

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.2: Exponents And Radicals

Problem 47E

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Question

Perform the indicated operations using the laws of exponents. Express the result using a single nonnegative exponent on 10.
-4
10-2. 10-7
109

Expert Solution

Step 1

Given expression is ${(\frac{10^{- 2} \cdot 10^{- 7}}{10^{9}})}^{- 4}$

We have to simplify the given expression.

Use property $a^{m} \cdot a^{n} = a^{m + n}$

Hence,

$\begin{matrix} {(\frac{10^{- 2} \cdot 10^{- 7}}{10^{9}})}^{- 4} = {(\frac{10^{- 2 - 7}}{10^{9}})}^{- 4} \\ = {(\frac{10^{- 9}}{10^{9}})}^{- 4} \\ = {(10^{- 9 - 9})}^{- 4} (Use property \frac{a^{m}}{a^{n}} = a^{m - n}) \\ = {(10^{- 18})}^{- 4} \end{matrix}$