which are the correct steps to follow to simply an exponential expression using the quotient rule of integer exponents?

To simplify an exponential expression using the Quotient Rule of integer exponents, you can follow these steps:

1. **Identify the Bases and Exponents**: Ensure the expression is in the form \(\frac{a^m}{a^n}\), where \(a\) is the base and \(m\) and \(n\) are the integer exponents.

2. **Apply the Quotient Rule**: The Quotient Rule states that when you divide two expressions with the same base, you can subtract the exponents. Specifically:
\[
\frac{a^m}{a^n} = a^{m-n}
\]

3. **Perform the Subtraction**: Calculate the difference in the exponents:
\[
m - n
\]

4. **Rewrite the Expression**: Replace the original expression with the result from the exponent subtraction:
\[
\frac{a^m}{a^n} = a^{m-n}
\]

5. **Final Simplification**: If needed, further simplify the expression based on the value of \(m - n\).

### Example:
Simplify \(\frac{x^5}{x^2}\).

1. Identify bases and exponents: Base is \(x\), \(m = 5\), \(n = 2\).
2. Apply the Quotient Rule:
\[
\frac{x^5}{x^2} = x^{5-2}
\]
3. Perform the subtraction:
\[
5 - 2 = 3
\]
4. Rewrite the expression:
\[
\frac{x^5}{x^2} = x^3
\]

So, the final simplified expression is \(x^3\).

Following these steps will help you simplify most exponential expressions involving the quotient rule effectively!