Answer all questions correctly.

Let's go through each question:

1. **Which of the following is an equivalent expression to \(5^*5^{-13}\) with only positive exponents?**

To find an equivalent expression, we use the property \(a^m \cdot a^n = a^{m+n}\).
Thus:
\[
5^1 \cdot 5^{-13} = 5^{1 - 13} = 5^{-12}
\]
For positive exponents, we rewrite it as:
\[
5^{-12} = \frac{1}{5^{12}}
\]

2. **Which property of exponents was used to generate the equivalent expression \(3^{14}\) from \(\frac{3^5}{3^{-9}}\)?**

We use the property of exponents which states that:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
Therefore, applying that:
\[
\frac{3^5}{3^{-9}} = 3^{5 - (-9)} = 3^{5 + 9} = 3^{14}
\]

3. **Which of the following is an equivalent expression to \(\frac{15^0 \cdot 7^{-2}}{(-4)^{-3}}\) with only positive exponents?**

We first simplify:
\(15^0 = 1\), so we have:
\[
\frac{1 \cdot 7^{-2}}{(-4)^{-3}} = \frac{7^{-2}}{(-4)^{-3}} = 7^{-2} \cdot (-4)^3
\]
Now rewrite it with positive exponents. The equivalent expression becomes:
\[
7^{-2} \cdot (-4)^3 = \frac{(-4)^3}{7^2}
\]

4. **Which of the following is the equivalent expression to \(\frac{(15^{-3} \cdot 4^{7})^0}{4^{-3}}\) that has been generated by applying the properties of integer exponents?**

Since any expression raised to the power of 0 is equal to 1:
\[
(15^{-3} \cdot 4^{7})^0 = 1
\]
Therefore:
\[
\frac{1}{4^{-3}} = 4^{3}
\]

5. **Which of the following is an equivalent expression to \(\frac{(2^{-3} \cdot 9^{3})^{-4}}{2^{9} \cdot 9^{-10}}\) with only positive exponents?**

First, simplify the numerator:
\[
(2^{-3} \cdot 9^{3})^{-4} = 2^{12} \cdot 9^{-12} = \frac{2^{12}}{9^{12}}
\]
Our expression now looks like:
\[
\frac{\frac{2^{12}}{9^{12}}}{2^{9} \cdot 9^{-10}} = \frac{2^{12}}{9^{12}} \cdot \frac{1}{2^{9} \cdot 9^{-10}} = \frac{2^{12}}{2^{9} \cdot 9^{12}} \cdot 9^{10}
\]
This ultimately equals:
\[
\frac{2^{12 - 9}}{9^{12 - 10}} = \frac{2^{3}}{9^{2}} = \frac{8}{81}
\]

Note that the exact answers to the multiple-choice questions would depend on the specific options available. However, these calculated forms with only positive exponents are general answers.

Give me just the answers. no explanation

1. \(\frac{1}{5^{12}}\)

2. \(\frac{a^m}{a^n} = a^{m-n}\)

3. \(\frac{(-4)^3}{7^2}\)

4. \(4^{3}\)

5. \(\frac{2^{3}}{9^{2}}\) or \(\frac{8}{81}\)