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The expression to solve is:

\[
\frac{5^m \cdot 5^2}{5^n}
\]
where \(m = 4\) and \(n = 3\).

### Step 1: Substitute the values of \(m\) and \(n\) into the expression:
\[
\frac{5^4 \cdot 5^2}{5^3}
\]

### Step 2: Apply the laws of exponents.
Recall that for multiplication, we add exponents:
\[
5^4 \cdot 5^2 = 5^{4+2} = 5^6
\]
So the expression becomes:
\[
\frac{5^6}{5^3}
\]

### Step 3: Simplify the division of exponents.
For division, we subtract exponents:
\[
\frac{5^6}{5^3} = 5^{6-3} = 5^3
\]

Thus, the final result is:
\[
5^3 = 125
\]

The answer is \(125\).

Would you like more details or have any questions?

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Here are 5 related questions you could explore:
1. What happens if \(m = 5\) and \(n = 2\)?
2. How does the division of powers work for other bases, like 7 or 10?
3. Can you explain the laws of exponents in more detail?
4. How would the result change if the exponents were negative?
5. What if the entire expression was raised to another exponent?

**Tip:** When working with powers, always remember to simplify using the exponent rules: add for multiplication and subtract for division.

If m = 4 and n = 3, find the value of the expression (5^m * 5^2) / 5^n

Learn how to simplify the expression (5^m * 5^2) / 5^n where m = 4 and n = 3. This step-by-step guide explores exponent laws and how to apply them. Suitable for students in Grades 8-10.

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