https://file.aiquickdraw.com/mathbot/file/1727405835665d9tgbbki.jpg

Let's analyze and solve the equation given in the image:

The equation is:

\[
5 \left( \frac{1}{5^3} \right) = 5(5^3)
\]

### Step-by-Step Explanation:

1. **Left Side:**
   \[
   5 \left( \frac{1}{5^3} \right) = \frac{5}{5^3}
   \]
   We simplify the expression \( \frac{5}{5^3} \). Since \( 5^3 = 5 \times 5 \times 5 = 125 \), this becomes:
   \[
   \frac{5}{5^3} = \frac{5}{125} = \frac{1}{25}
   \]
   
2. **Right Side:**
   \[
   5(5^3) = 5 \times 5^3
   \]
   We know \( 5^3 = 125 \), so:
   \[
   5 \times 125 = 625
   \]

3. **Comparison:**
   Now we compare both sides:
   - Left side: \( \frac{1}{25} \)
   - Right side: \( 625 \)

Clearly, \( \frac{1}{25} \neq 625 \).

### Conclusion:
The equation \( 5 \left( \frac{1}{5^3} \right) = 5(5^3) \) is **false**, because the two sides are not equal.

Would you like further clarification or more details on any of the steps?

Here are 5 related questions to deepen your understanding:
1. How do we simplify expressions with powers of numbers?
2. Why is \( \frac{5}{5^3} \) simplified to \( \frac{1}{25} \)?
3. What are the rules for multiplying and dividing exponents?
4. How do negative exponents relate to fractions?
5. Can the equation \( 5 \left( \frac{1}{5^3} \right) = 5(5^3) \) ever hold true under different conditions?

**Tip:** Remember, when working with exponents and fractions, always simplify powers before performing any multiplication or division!

Explore whether 5(1/5^3) equals 5(5^3) with a detailed step-by-step solution. Learn key concepts like exponentiation and simplification of fractions. This problem is ideal for students in Grades 6-8.

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