To express [tex]\(\frac{x^m}{x^n}\)[/tex] as a power of [tex]\(x\)[/tex], we can use the rules of exponents. Let's go through the solution step by step:
1. Understand the problem:
We need to simplify the expression [tex]\(\frac{x^m}{x^n}\)[/tex], where [tex]\(x\)[/tex] is the base and [tex]\(m\)[/tex] and [tex]\(n\)[/tex] are the exponents.
2. Apply the quotient rule of exponents:
The quotient rule of exponents states that when you divide powers with the same base, you subtract the exponents. The rule is:
[tex]\[
\frac{a^m}{a^n} = a^{m-n}
\][/tex]
Here, the base [tex]\(a\)[/tex] is the same in both the numerator and the denominator.
3. Simplify the given expression:
Using the quotient rule of exponents, we can simplify [tex]\(\frac{x^m}{x^n}\)[/tex] as follows:
[tex]\[
\frac{x^m}{x^n} = x^{m-n}
\][/tex]
So, the expression [tex]\(\frac{x^m}{x^n}\)[/tex] can be written as [tex]\(x^{m-n}\)[/tex].
