Question
1. Apply the Property of Negative Integer Exponents to rewrite 15^−38%0D%0A15%0D%0A−%0D%0A38%0D%0A as an expression with positive exponents only.
2. Apply the Property of Negative Integer Exponents to rewrite 9^−23%0D%0A9%0D%0A−%0D%0A23%0D%0A as an expression with positive exponents only.
3. Apply the Property of Negative Integer Exponents to solve 3^−4%0D%0A3%0D%0A−%0D%0A4%0D%0A. The answer should not contain any exponent expression or decimals.(1 point)%0D%0A3−4=%0D%0A3%0D%0A−%0D%0A4%0D%0A=
4. Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7^−3⋅7^−5%0D%0A7%0D%0A−%0D%0A3%0D%0A⋅%0D%0A7%0D%0A−%0D%0A5%0D%0A with positive exponents only.
5. Apply the Property of Negative Integer Exponents to generate an expression equivalent to 5^−9/4^−12%0D%0A5%0D%0A−%0D%0A9%0D%0A4%0D%0A−%0D%0A12%0D%0A with positive exponents only.
2. Apply the Property of Negative Integer Exponents to rewrite 9^−23%0D%0A9%0D%0A−%0D%0A23%0D%0A as an expression with positive exponents only.
3. Apply the Property of Negative Integer Exponents to solve 3^−4%0D%0A3%0D%0A−%0D%0A4%0D%0A. The answer should not contain any exponent expression or decimals.(1 point)%0D%0A3−4=%0D%0A3%0D%0A−%0D%0A4%0D%0A=
4. Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7^−3⋅7^−5%0D%0A7%0D%0A−%0D%0A3%0D%0A⋅%0D%0A7%0D%0A−%0D%0A5%0D%0A with positive exponents only.
5. Apply the Property of Negative Integer Exponents to generate an expression equivalent to 5^−9/4^−12%0D%0A5%0D%0A−%0D%0A9%0D%0A4%0D%0A−%0D%0A12%0D%0A with positive exponents only.
Answers
Answer
1. Which of the following is developed to be equivalent to 1/8^5?(1 point)%0D%0AResponses
5^-8
8^-5
8^5
8 1/5
2. Which of the following is equivalent to 6^−2?
1/2^6
1/6-2
36
1/36
3. Which of the following is an equivalent expression to 13^−5 x 13^−11 with only positive exponents, generated by applying the properties of exponents?
1/13^16
1/26^16
1/13^6
1/26^6
4. Which of the following is an equivalent expression to 14^−7/9^−13 with only positive exponents, generated by applying the Property of Negative Integer Exponents?
9^13/14^7
1/9^13 x 14^-7
14^7/9^13
14^17 x 9^13
5. Which of the following is an equivalent expression to 7^3/25^−4 with only positive exponents, generated by applying the Property of Negative Integer Exponents?
25^4/7^3
25^4/7^-3
7^3 x 25^4
7^3/25^4
5^-8
8^-5
8^5
8 1/5
2. Which of the following is equivalent to 6^−2?
1/2^6
1/6-2
36
1/36
3. Which of the following is an equivalent expression to 13^−5 x 13^−11 with only positive exponents, generated by applying the properties of exponents?
1/13^16
1/26^16
1/13^6
1/26^6
4. Which of the following is an equivalent expression to 14^−7/9^−13 with only positive exponents, generated by applying the Property of Negative Integer Exponents?
9^13/14^7
1/9^13 x 14^-7
14^7/9^13
14^17 x 9^13
5. Which of the following is an equivalent expression to 7^3/25^−4 with only positive exponents, generated by applying the Property of Negative Integer Exponents?
25^4/7^3
25^4/7^-3
7^3 x 25^4
7^3/25^4
Answer
PERFECT!!!
Answered by
GPT-4o mini
Let's solve each of these problems step by step using the Property of Negative Integer Exponents, which states that \( a^{-n} = \frac{1}{a^n} \).
1. **Rewriting \( 15^{-38} \)**:
\[
15^{-38} = \frac{1}{15^{38}}
\]
2. **Rewriting \( 9^{-23} \)**:
\[
9^{-23} = \frac{1}{9^{23}}
\]
3. **Solving \( 3^{-4} \)**:
\[
3^{-4} = \frac{1}{3^{4}} = \frac{1}{81}
\]
4. **Generating an expression for \( 7^{-3} \cdot 7^{-5} \)**:
\[
7^{-3} \cdot 7^{-5} = 7^{-3 + (-5)} = 7^{-8}
\]
To convert it to positive exponent:
\[
7^{-8} = \frac{1}{7^8}
\]
5. **Generating an expression for \( \frac{5^{-9}}{4^{-12}} \)**:
\[
\frac{5^{-9}}{4^{-12}} = 5^{-9} \cdot 4^{12}
\]
Rewriting \( 5^{-9} \):
\[
= \frac{4^{12}}{5^9}
\]
To summarize:
1. \( 15^{-38} = \frac{1}{15^{38}} \)
2. \( 9^{-23} = \frac{1}{9^{23}} \)
3. \( 3^{-4} = \frac{1}{81} \)
4. \( 7^{-3} \cdot 7^{-5} = \frac{1}{7^8} \)
5. \( \frac{5^{-9}}{4^{-12}} = \frac{4^{12}}{5^9} \)
1. **Rewriting \( 15^{-38} \)**:
\[
15^{-38} = \frac{1}{15^{38}}
\]
2. **Rewriting \( 9^{-23} \)**:
\[
9^{-23} = \frac{1}{9^{23}}
\]
3. **Solving \( 3^{-4} \)**:
\[
3^{-4} = \frac{1}{3^{4}} = \frac{1}{81}
\]
4. **Generating an expression for \( 7^{-3} \cdot 7^{-5} \)**:
\[
7^{-3} \cdot 7^{-5} = 7^{-3 + (-5)} = 7^{-8}
\]
To convert it to positive exponent:
\[
7^{-8} = \frac{1}{7^8}
\]
5. **Generating an expression for \( \frac{5^{-9}}{4^{-12}} \)**:
\[
\frac{5^{-9}}{4^{-12}} = 5^{-9} \cdot 4^{12}
\]
Rewriting \( 5^{-9} \):
\[
= \frac{4^{12}}{5^9}
\]
To summarize:
1. \( 15^{-38} = \frac{1}{15^{38}} \)
2. \( 9^{-23} = \frac{1}{9^{23}} \)
3. \( 3^{-4} = \frac{1}{81} \)
4. \( 7^{-3} \cdot 7^{-5} = \frac{1}{7^8} \)
5. \( \frac{5^{-9}}{4^{-12}} = \frac{4^{12}}{5^9} \)
Answered by
GPT-4o mini
Let’s analyze and solve each question to identify the correct responses:
1. **Which of the following is developed to be equivalent to \( \frac{1}{8^5} \)?**
- To rewrite \( \frac{1}{8^5} \) using properties of exponents:
\[
\frac{1}{8^5} = 8^{-5}
\]
- **Correct Answer:** **8^-5**
2. **Which of the following is equivalent to \( 6^{-2} \)?**
- To rewrite \( 6^{-2} \):
\[
6^{-2} = \frac{1}{6^2} = \frac{1}{36}
\]
- **Correct Answer:** **1/36**
3. **Which of the following is an equivalent expression to \( 13^{-5} \times 13^{-11} \) with only positive exponents?**
- Applying the properties of exponents:
\[
13^{-5} \times 13^{-11} = 13^{-5 + (-11)} = 13^{-16}
\]
\[
13^{-16} = \frac{1}{13^{16}}
\]
- **Correct Answer:** **1/13^16**
4. **Which of the following is an equivalent expression to \( \frac{14^{-7}}{9^{-13}} \) with only positive exponents?**
- Rewriting using properties of exponents:
\[
\frac{14^{-7}}{9^{-13}} = 14^{-7} \times 9^{13} = \frac{9^{13}}{14^{7}}
\]
- **Correct Answer:** **9^13/14^7**
5. **Which of the following is an equivalent expression to \( \frac{7^{3}}{25^{-4}} \) with only positive exponents?**
- Rewriting using properties of exponents:
\[
\frac{7^{3}}{25^{-4}} = 7^{3} \times 25^{4} = 7^3 \cdot 25^4
\]
- **Correct Answer:** **7^3 x 25^4**
**Summary of Answers:**
1. **8^-5**
2. **1/36**
3. **1/13^16**
4. **9^13/14^7**
5. **7^3 x 25^4**
1. **Which of the following is developed to be equivalent to \( \frac{1}{8^5} \)?**
- To rewrite \( \frac{1}{8^5} \) using properties of exponents:
\[
\frac{1}{8^5} = 8^{-5}
\]
- **Correct Answer:** **8^-5**
2. **Which of the following is equivalent to \( 6^{-2} \)?**
- To rewrite \( 6^{-2} \):
\[
6^{-2} = \frac{1}{6^2} = \frac{1}{36}
\]
- **Correct Answer:** **1/36**
3. **Which of the following is an equivalent expression to \( 13^{-5} \times 13^{-11} \) with only positive exponents?**
- Applying the properties of exponents:
\[
13^{-5} \times 13^{-11} = 13^{-5 + (-11)} = 13^{-16}
\]
\[
13^{-16} = \frac{1}{13^{16}}
\]
- **Correct Answer:** **1/13^16**
4. **Which of the following is an equivalent expression to \( \frac{14^{-7}}{9^{-13}} \) with only positive exponents?**
- Rewriting using properties of exponents:
\[
\frac{14^{-7}}{9^{-13}} = 14^{-7} \times 9^{13} = \frac{9^{13}}{14^{7}}
\]
- **Correct Answer:** **9^13/14^7**
5. **Which of the following is an equivalent expression to \( \frac{7^{3}}{25^{-4}} \) with only positive exponents?**
- Rewriting using properties of exponents:
\[
\frac{7^{3}}{25^{-4}} = 7^{3} \times 25^{4} = 7^3 \cdot 25^4
\]
- **Correct Answer:** **7^3 x 25^4**
**Summary of Answers:**
1. **8^-5**
2. **1/36**
3. **1/13^16**
4. **9^13/14^7**
5. **7^3 x 25^4**
Answered by
GPT-4o mini
Thank you! I'm glad you found the answers helpful. If you have any more questions or need further assistance, feel free to ask!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.