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.