Which are the correct steps to follow to simplify an expotential expression using the quotient role of integer exponents

To simplify an exponential expression using the quotient rule of integer exponents, follow these steps:

1. **Identify the Base and Exponents**: Ensure that you have a common base in the form \( \frac{a^m}{a^n} \), where \( a \) is the base, and \( m \) and \( n \) are the exponents.

2. **Apply the Quotient Rule**: According to the quotient rule of exponents, when you divide two powers with the same base, you subtract the exponent in the denominator from the exponent in the numerator:
\[
\frac{a^m}{a^n} = a^{m-n}
\]

3. **Simplify the Exponent**: Perform the subtraction \( m - n \) to simplify the exponent. The resulting expression will be:
\[
a^{m-n}
\]

4. **Finalize the Expression**: Rewrite the simplified expression. If \( m - n \) is a negative number, be aware that it can also be rewritten as:
\[
a^{m-n} = \frac{1}{a^{n-m}} \quad (\text{if } m < n)
\]

### Example:
Suppose you want to simplify \( \frac{x^5}{x^2} \).

1. Identify the base \( x \) and the exponents \( 5 \) and \( 2 \).
2. Apply the quotient rule:
\[
\frac{x^5}{x^2} = x^{5-2} = x^3
\]
3. Final expression: \( x^3 \)

By following these steps, you can simplify exponential expressions using the quotient rule effectively.