Question
answer all questions correctly.
Which of the following is developed to be equivalent to 1 over 8^5?
Which of the following is equivalent to 6^-2?
Which of the following is an equivalent expression to 13^-5*13^11 with only positive exponents, generated by applying the properties of exponents?
Which of the following is an equivalent expression to 14^-7 over 9^-13 with only positive exponents, generated by applying the property of negative integer exponents?
Which of the following is an equivalent expression to 7^3 over 25^-4 with only positive exponents, generated by applying the property of negative integer exponents?
Which of the following is developed to be equivalent to 1 over 8^5?
Which of the following is equivalent to 6^-2?
Which of the following is an equivalent expression to 13^-5*13^11 with only positive exponents, generated by applying the properties of exponents?
Which of the following is an equivalent expression to 14^-7 over 9^-13 with only positive exponents, generated by applying the property of negative integer exponents?
Which of the following is an equivalent expression to 7^3 over 25^-4 with only positive exponents, generated by applying the property of negative integer exponents?
Answers
GPT-4o mini
Let's address each question step by step:
1. **Which of the following is developed to be equivalent to 1 over 8^5?**
\[
1 \div 8^5 = 8^{-5}
\]
2. **Which of the following is equivalent to 6^-2?**
\[
6^{-2} = \frac{1}{6^2} = \frac{1}{36}
\]
3. **Which of the following is an equivalent expression to 13^-5*13^11 with only positive exponents?**
By applying the property of exponents \( a^m \cdot a^n = a^{m+n} \):
\[
13^{-5} \cdot 13^{11} = 13^{-5 + 11} = 13^{6}
\]
4. **Which of the following is an equivalent expression to 14^-7 over 9^-13 with only positive exponents?**
Applying the properties of negative exponents:
\[
\frac{14^{-7}}{9^{-13}} = \frac{1}{14^7} \cdot 9^{13} = \frac{9^{13}}{14^7}
\]
5. **Which of the following is an equivalent expression to 7^3 over 25^-4 with only positive exponents?**
Using the properties of negative exponents:
\[
\frac{7^3}{25^{-4}} = 7^3 \cdot 25^4 = 7^3 \cdot 25^4
\]
In summary, the answers are:
1. \( 8^{-5} \)
2. \( \frac{1}{36} \)
3. \( 13^{6} \)
4. \( \frac{9^{13}}{14^7} \)
5. \( 7^3 \cdot 25^4 \)
1. **Which of the following is developed to be equivalent to 1 over 8^5?**
\[
1 \div 8^5 = 8^{-5}
\]
2. **Which of the following is equivalent to 6^-2?**
\[
6^{-2} = \frac{1}{6^2} = \frac{1}{36}
\]
3. **Which of the following is an equivalent expression to 13^-5*13^11 with only positive exponents?**
By applying the property of exponents \( a^m \cdot a^n = a^{m+n} \):
\[
13^{-5} \cdot 13^{11} = 13^{-5 + 11} = 13^{6}
\]
4. **Which of the following is an equivalent expression to 14^-7 over 9^-13 with only positive exponents?**
Applying the properties of negative exponents:
\[
\frac{14^{-7}}{9^{-13}} = \frac{1}{14^7} \cdot 9^{13} = \frac{9^{13}}{14^7}
\]
5. **Which of the following is an equivalent expression to 7^3 over 25^-4 with only positive exponents?**
Using the properties of negative exponents:
\[
\frac{7^3}{25^{-4}} = 7^3 \cdot 25^4 = 7^3 \cdot 25^4
\]
In summary, the answers are:
1. \( 8^{-5} \)
2. \( \frac{1}{36} \)
3. \( 13^{6} \)
4. \( \frac{9^{13}}{14^7} \)
5. \( 7^3 \cdot 25^4 \)