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### Find the Mistake Below are several mathematical expressions. Each expression contains an error. Your task is to identify the mistake in each one. 1. \( b^3 \cdot b^4 = b^{12} \) 2. \( \frac{5^{16}}{5^4} = 5^4 \) 3. \( (a + b)^2 = a^2 + b^2 \) 4. \( (4a)^3 = 4a^3 \) 5. \( 3^2 \cdot 3^4 = 9^6 \) 6. \( b^{-n} = -\frac{1}{b^n} \) 7. \( (a + b)^{-1} = \frac{1}{a} + \frac{1}{b} \) 8. \( (2b^2)^3 = 6b^5 \) #### Explanation of Mistakes: 1. **Error in Multiplication of Exponents**: Correct result should be \( b^{3+4} = b^7 \). 2. **Error in Division of Exponents**: Correct result should be \( \frac{5^{16}}{5^4} = 5^{16-4} = 5^{12} \). 3. **Error in Expansion of Binomial**: Correct result should be \( (a + b)^2 = a^2 + 2ab + b^2 \). 4. **Error in Cubing a Product**: Correct result should be \( (4a)^3 = 4^3a^3 = 64a^3 \). 5. **Error in Multiplication of Exponents**: Correct result should be \( 3^2 \cdot 3^4 = 3^{2+4} = 3^6 \). 6. **Error in Negative Exponent Rule**: Correct result should be \( b^{-n} = \frac{1}{b^n} \). The negative exponent does not introduce a negative sign in the fraction. 7. **Error in Reciprocal of Sum**: Correct result should be \( (a + b)^{-1} = \frac{1}{a + b} \). 8. **Error in Exponential Rule for Products**: Correct result should be \( (2b^2)^3 = 2^3(b^

### Find the Mistake Below are several mathematical expressions. Each expression contains an error. Your task is to identify the mistake in each one. 1. \( b^3 \cdot b^4 = b^{12} \) 2. \( \frac{5^{16}}{5^4} = 5^4 \) 3. \( (a + b)^2 = a^2 + b^2 \) 4. \( (4a)^3 = 4a^3 \) 5. \( 3^2 \cdot 3^4 = 9^6 \) 6. \( b^{-n} = -\frac{1}{b^n} \) 7. \( (a + b)^{-1} = \frac{1}{a} + \frac{1}{b} \) 8. \( (2b^2)^3 = 6b^5 \) #### Explanation of Mistakes: 1. **Error in Multiplication of Exponents**: Correct result should be \( b^{3+4} = b^7 \). 2. **Error in Division of Exponents**: Correct result should be \( \frac{5^{16}}{5^4} = 5^{16-4} = 5^{12} \). 3. **Error in Expansion of Binomial**: Correct result should be \( (a + b)^2 = a^2 + 2ab + b^2 \). 4. **Error in Cubing a Product**: Correct result should be \( (4a)^3 = 4^3a^3 = 64a^3 \). 5. **Error in Multiplication of Exponents**: Correct result should be \( 3^2 \cdot 3^4 = 3^{2+4} = 3^6 \). 6. **Error in Negative Exponent Rule**: Correct result should be \( b^{-n} = \frac{1}{b^n} \). The negative exponent does not introduce a negative sign in the fraction. 7. **Error in Reciprocal of Sum**: Correct result should be \( (a + b)^{-1} = \frac{1}{a + b} \). 8. **Error in Exponential Rule for Products**: Correct result should be \( (2b^2)^3 = 2^3(b^

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Find the Mistake Below are several mathematical expressions. Each expression contains an error. Your task is to identify the mistake in each one. 1. \( b^3 \cdot b^4 = b^{12} \) 2. \( \frac{5^{16}}{5^4} = 5^4 \) 3. \( (a + b)^2 = a^2 + b^2 \) 4. \( (4a)^3 = 4a^3 \) 5. \( 3^2 \cdot 3^4 = 9^6 \) 6. \( b^{-n} = -\frac{1}{b^n} \) 7. \( (a + b)^{-1} = \frac{1}{a} + \frac{1}{b} \) 8. \( (2b^2)^3 = 6b^5 \) #### Explanation of Mistakes: 1. **Error in Multiplication of Exponents**: Correct result should be \( b^{3+4} = b^7 \). 2. **Error in Division of Exponents**: Correct result should be \( \frac{5^{16}}{5^4} = 5^{16-4} = 5^{12} \). 3. **Error in Expansion of Binomial**: Correct result should be \( (a + b)^2 = a^2 + 2ab + b^2 \). 4. **Error in Cubing a Product**: Correct result should be \( (4a)^3 = 4^3a^3 = 64a^3 \). 5. **Error in Multiplication of Exponents**: Correct result should be \( 3^2 \cdot 3^4 = 3^{2+4} = 3^6 \). 6. **Error in Negative Exponent Rule**: Correct result should be \( b^{-n} = \frac{1}{b^n} \). The negative exponent does not introduce a negative sign in the fraction. 7. **Error in Reciprocal of Sum**: Correct result should be \( (a + b)^{-1} = \frac{1}{a + b} \). 8. **Error in Exponential Rule for Products**: Correct result should be \( (2b^2)^3 = 2^3(b^
Transcribed Image Text:### Find the Mistake Below are several mathematical expressions. Each expression contains an error. Your task is to identify the mistake in each one. 1. \( b^3 \cdot b^4 = b^{12} \) 2. \( \frac{5^{16}}{5^4} = 5^4 \) 3. \( (a + b)^2 = a^2 + b^2 \) 4. \( (4a)^3 = 4a^3 \) 5. \( 3^2 \cdot 3^4 = 9^6 \) 6. \( b^{-n} = -\frac{1}{b^n} \) 7. \( (a + b)^{-1} = \frac{1}{a} + \frac{1}{b} \) 8. \( (2b^2)^3 = 6b^5 \) #### Explanation of Mistakes: 1. **Error in Multiplication of Exponents**: Correct result should be \( b^{3+4} = b^7 \). 2. **Error in Division of Exponents**: Correct result should be \( \frac{5^{16}}{5^4} = 5^{16-4} = 5^{12} \). 3. **Error in Expansion of Binomial**: Correct result should be \( (a + b)^2 = a^2 + 2ab + b^2 \). 4. **Error in Cubing a Product**: Correct result should be \( (4a)^3 = 4^3a^3 = 64a^3 \). 5. **Error in Multiplication of Exponents**: Correct result should be \( 3^2 \cdot 3^4 = 3^{2+4} = 3^6 \). 6. **Error in Negative Exponent Rule**: Correct result should be \( b^{-n} = \frac{1}{b^n} \). The negative exponent does not introduce a negative sign in the fraction. 7. **Error in Reciprocal of Sum**: Correct result should be \( (a + b)^{-1} = \frac{1}{a + b} \). 8. **Error in Exponential Rule for Products**: Correct result should be \( (2b^2)^3 = 2^3(b^
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