Chemistry
Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
Bartleby Related Questions Icon

Related questions

bartleby

Concept explainers

Question
**Powers and Roots in Chemistry Calculations**

It is sometimes necessary to take powers or roots to solve chemistry problems.

Take powers and roots as needed on your calculator to complete the following:

\[ a = 2.23^5 \]

\[ b^5 = 84.7 \]

\[ c = 2.00^{4.70} \]

\[ d^{4.07} = 613 \]

**Fill in the results:**

\[ a = \]

\[ b = \]

\[ c = \]

\[ d = \]
expand button
Transcribed Image Text:**Powers and Roots in Chemistry Calculations** It is sometimes necessary to take powers or roots to solve chemistry problems. Take powers and roots as needed on your calculator to complete the following: \[ a = 2.23^5 \] \[ b^5 = 84.7 \] \[ c = 2.00^{4.70} \] \[ d^{4.07} = 613 \] **Fill in the results:** \[ a = \] \[ b = \] \[ c = \] \[ d = \]
### Exponent Operations Exercise

Complete the following operations by filling in the value of the exponent for the result:

1. \(\frac{1}{10^{-4}} = 10^{\boxed{}}\)

2. \((10^3)(10^4) = 10^{\boxed{}}\)

3. \(\frac{10^7}{10^{-1}} = 10^{\boxed{}}\)

4. \((10^{-4})^2 = 10^{\boxed{}}\)

**Explanation of each problem:**

1. The first problem involves the division of 1 by \(10^{-4}\). To solve for \(10^{\boxed{}}\), you need to use the property of exponents that states \( \frac{1}{a^{-b}} = a^{b} \).

2. The second problem asks you to multiply \(10^3\) by \(10^4\). Using the property of exponents that states \(a^m \cdot a^n = a^{m+n}\), you will find the exponent for \(10\) in the result.

3. The third problem involves dividing \(10^7\) by \(10^{-1}\). By applying the exponent division rule \( \frac{a^m}{a^n} = a^{m-n} \), you can determine the exponent for \(10\).

4. The fourth problem requires you to raise \(10^{-4}\) to the power of 2. This can be solved using the property \( (a^m)^n = a^{mn} \).

Place your answers in the provided boxes to complete the operations.
expand button
Transcribed Image Text:### Exponent Operations Exercise Complete the following operations by filling in the value of the exponent for the result: 1. \(\frac{1}{10^{-4}} = 10^{\boxed{}}\) 2. \((10^3)(10^4) = 10^{\boxed{}}\) 3. \(\frac{10^7}{10^{-1}} = 10^{\boxed{}}\) 4. \((10^{-4})^2 = 10^{\boxed{}}\) **Explanation of each problem:** 1. The first problem involves the division of 1 by \(10^{-4}\). To solve for \(10^{\boxed{}}\), you need to use the property of exponents that states \( \frac{1}{a^{-b}} = a^{b} \). 2. The second problem asks you to multiply \(10^3\) by \(10^4\). Using the property of exponents that states \(a^m \cdot a^n = a^{m+n}\), you will find the exponent for \(10\) in the result. 3. The third problem involves dividing \(10^7\) by \(10^{-1}\). By applying the exponent division rule \( \frac{a^m}{a^n} = a^{m-n} \), you can determine the exponent for \(10\). 4. The fourth problem requires you to raise \(10^{-4}\) to the power of 2. This can be solved using the property \( (a^m)^n = a^{mn} \). Place your answers in the provided boxes to complete the operations.
Expert Solution
Check Mark
Knowledge Booster
Background pattern image
Chemistry
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Chemistry
Chemistry
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Cengage Learning
Text book image
Chemistry
Chemistry
ISBN:9781259911156
Author:Raymond Chang Dr., Jason Overby Professor
Publisher:McGraw-Hill Education
Text book image
Principles of Instrumental Analysis
Chemistry
ISBN:9781305577213
Author:Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:Cengage Learning
Text book image
Organic Chemistry
Chemistry
ISBN:9780078021558
Author:Janice Gorzynski Smith Dr.
Publisher:McGraw-Hill Education
Text book image
Chemistry: Principles and Reactions
Chemistry
ISBN:9781305079373
Author:William L. Masterton, Cecile N. Hurley
Publisher:Cengage Learning
Text book image
Elementary Principles of Chemical Processes, Bind...
Chemistry
ISBN:9781118431221
Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:WILEY