Question

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

Answer 1

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!