how do i write 1/125 as a single power of 5

To express \( \frac{1}{125} \) as a single power of 5, follow these steps:

1. First, recognize that \( 125 = 5^3 \), because \( 5 \times 5 \times 5 = 125 \).
   
2. Therefore, \( \frac{1}{125} = \frac{1}{5^3} \).

3. Use the negative exponent rule: \( \frac{1}{a^n} = a^{-n} \).

4. Applying this rule, \( \frac{1}{5^3} = 5^{-3} \).

So, \( \frac{1}{125} = 5^{-3} \).

Would you like more details on negative exponents or the steps involved?

Here are some related questions:
1. What is \( \frac{1}{625} \) as a power of 5?
2. How do you express \( \frac{1}{32} \) as a power of 2?
3. How do you simplify \( 5^{-3} \times 5^2 \)?
4. What is the result of \( (5^{-2})^3 \)?
5. How do you convert a decimal like 0.008 to a power of 10?

**Tip:** When working with powers, negative exponents indicate the reciprocal of the base raised to the positive exponent.

Learn how to express 1/125 as a single power of 5 using the negative exponent rule. This detailed explanation walks you through recognizing that 125 is 5^3 and applying the reciprocal and negative exponent theorems. Perfect for students in Grades 6-8.

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