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!