Question

Question 1
Using the properties of exponents, write an equivalent expression.

(3/5)−3=
(1 point)
Responses

12527
125 over 27

27
27

−12527
negative 125 over 27

−27125
negative 27 over 125
Question 2
Show all work or steps from the problem above to receive full credit. You can type your answer in the box below or upload an image of your handwritten work using the icon on the tool bar. If you need math characters, click on the icon on the tool bar. (3 points)

Answer 1

### Question 1

We start with the expression \( (3/5)^{-3} \).

Using the property of exponents, we know that \( a^{-n} = \frac{1}{a^n} \). Therefore, we can rewrite \( (3/5)^{-3} \):

\[
(3/5)^{-3} = \frac{1}{(3/5)^3}
\]

Next, we need to calculate \( (3/5)^3 \):

\[
(3/5)^3 = \frac{3^3}{5^3} = \frac{27}{125}
\]

Putting this into our expression, we have:

\[
(3/5)^{-3} = \frac{1}{(3/5)^3} = \frac{1}{\frac{27}{125}} = \frac{125}{27}
\]

Thus, the equivalent expression is:

\[
(3/5)^{-3} = \frac{125}{27}
\]

So the correct response is **125 over 27**.

---

### Question 2

Here are the steps rewritten clearly:

1. Start with the expression: \( (3/5)^{-3} \).
2. Apply the property of exponents: \( a^{-n} = \frac{1}{a^n} \).
- So, \( (3/5)^{-3} = \frac{1}{(3/5)^{3}} \).
3. Calculate \( (3/5)^{3} \):
- \( (3/5)^{3} = \frac{3^3}{5^3} = \frac{27}{125} \).
4. Substitute back into the equation:
- \( (3/5)^{-3} = \frac{1}{\frac{27}{125}} \).
5. To find \( \frac{1}{\frac{27}{125}} \), we flip the fraction:
- \( \frac{1}{\frac{27}{125}} = \frac{125}{27} \).

Thus, the equivalent expression we derive is:

\[
\boxed{\frac{125}{27}}
\]