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.

Question

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.

Answer 1

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. \( \frac{5^{-9}}{4^{-12}} = \frac{4^{12}}{5^9} \)

Answer 2

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

Answer 3

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

Answer 4

PERFECT!!!

Answer 5

Thank you! I'm glad you found the answers helpful. If you have any more questions or need further assistance, feel free to ask!