https://file.aiquickdraw.com/mathbot/file/1726614563661ekitd23q.jpg

The question in the image is asking which expression decomposes \( \frac{1}{125} \) into a product of powers.

Let's break it down:

We know that \( 125 = 5^3 \), so:

\[
\frac{1}{125} = \frac{1}{5^3} = 5^{-3}
\]

Now, looking at the multiple-choice options:

1. \( 3^{-1} \times 5^{-2} \)
2. \( 5^{-1} \times 5^{-2} \)
3. \( 5^{-1} \times 2^{-2} \)

The correct decomposition of \( 5^{-3} \) into a product of powers is \( 5^{-1} \times 5^{-2} \) because:

\[
5^{-1} \times 5^{-2} = 5^{(-1) + (-2)} = 5^{-3}
\]

Thus, the correct answer is:

**Option 2: \( 5^{-1} \times 5^{-2} \)**.

Would you like a more detailed explanation or have any questions? 

Here are 5 questions to expand on this concept:
1. What is the rule for multiplying powers with the same base?
2. How do you handle negative exponents when simplifying expressions?
3. Can \( 125 \) be expressed as a different base besides 5?
4. What happens if the exponents are positive instead of negative?
5. How do you simplify \( \frac{1}{x^3} \) for any base \( x \)?

**Tip**: Always remember that dividing by a number raised to a power is the same as multiplying by that number with a negative exponent.

Which shows 1/125 decomposed into a product of powers?

Learn how to decompose 1/125 into a product of powers by applying properties of exponents. This problem explores negative exponents and exponent rules, suitable for Grade 7-8 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation