To simplify an expression like (x^m)/(x^n), which rule applies?

To simplify the expression ( \frac{x^m}{x^n} ), the rule that applies is known as the Quotient of Powers. This rule states that when you divide two expressions with the same base, you can subtract the exponent in the denominator from the exponent in the numerator.

Mathematically, this is expressed as:

[

\frac{x^m}{x^n} = x^{m-n}

]

This operation is based on the principle that you have a total of ( m ) factors of ( x ) in the numerator and ( n ) factors of ( x ) in the denominator. When you cancel out the ( n ) factors of ( x ) in the denominator from the ( m ) factors in the numerator, you are left with ( m - n ) factors of ( x ), leading to ( x^{m-n} ).

Understanding this rule is crucial for simplifying expressions that involve division of exponential terms, especially when working with algebraic expressions in more advanced contexts.