Chapter3: Using Spreadsheets In Analytical Chemistry
Section: Chapter Questions
Problem 3.6QAP
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![### Exponent Value Problem
**Question:**
What is the value of the exponent in the answer?
**Expression:**
\[ \frac{10^4}{(10^1)(10^{-7})} \]
**Options:**
- \( \circ \) 12
- \( \circ \) 10
- \( \circ \) -2
- \( \circ \) -4
**Explanation:**
To solve this problem, we need to apply the properties of exponents. Recall that when dividing like bases, we subtract the exponent of the denominator from the exponent of the numerator. Similarly, when multiplying like bases, we add the exponents.
Step-by-Step Solution:
1. **Initial Expression:**
\[ \frac{10^4}{(10^1)(10^{-7})} \]
2. **Simplify the Denominator:**
Combine the exponents in the denominator:
\[ 10^1 \times 10^{-7} = 10^{1 + (-7)} = 10^{-6} \]
3. **Simplify the overall expression:**
Now, the expression simplifies to:
\[ \frac{10^4}{10^{-6}} \]
4. **Apply the Division Rule of Exponents:**
Divide by subtracting the exponents:
\[ 10^{4 - (-6)} = 10^{4 + 6} = 10^{10} \]
Thus, the value of the exponent is **10**.
**Correct Option:**
- \( \circ \) 10](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7679d56-1d29-4c41-991e-162e3fac834d%2Fc2640dcb-2a40-4fa9-a097-27e4c9ac1c04%2Fvbz2pgr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Exponent Value Problem
**Question:**
What is the value of the exponent in the answer?
**Expression:**
\[ \frac{10^4}{(10^1)(10^{-7})} \]
**Options:**
- \( \circ \) 12
- \( \circ \) 10
- \( \circ \) -2
- \( \circ \) -4
**Explanation:**
To solve this problem, we need to apply the properties of exponents. Recall that when dividing like bases, we subtract the exponent of the denominator from the exponent of the numerator. Similarly, when multiplying like bases, we add the exponents.
Step-by-Step Solution:
1. **Initial Expression:**
\[ \frac{10^4}{(10^1)(10^{-7})} \]
2. **Simplify the Denominator:**
Combine the exponents in the denominator:
\[ 10^1 \times 10^{-7} = 10^{1 + (-7)} = 10^{-6} \]
3. **Simplify the overall expression:**
Now, the expression simplifies to:
\[ \frac{10^4}{10^{-6}} \]
4. **Apply the Division Rule of Exponents:**
Divide by subtracting the exponents:
\[ 10^{4 - (-6)} = 10^{4 + 6} = 10^{10} \]
Thus, the value of the exponent is **10**.
**Correct Option:**
- \( \circ \) 10
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