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Complete the following operations by filling in the value of the exponent for the result: 1 10-4 = 10 (10³) (10¹) = 107 10-1 (10-4) ² 10 = 10 = 10

Complete the following operations by filling in the value of the exponent for the result: 1 10-4 = 10 (10³) (10¹) = 107 10-1 (10-4) ² 10 = 10 = 10

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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**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:** \[ a = \] \[ b = \] \[ c = \] \[ d = \]
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.
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.
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