Problem
Simplify the polynomial expression \(\frac{x^5}{x^2}\) and rewrite it using negative exponents.
Solution
Step 1 ：First, we apply the division rule of exponents, which says that \(\frac{a^n}{a^m} = a^{n-m}\). So the expression becomes \(x^{5-2} = x^3\).
Step 2 ：Next, to rewrite \(x^3\) using negative exponents, we consider that for any non-zero number a, \(a^{-n} = \frac{1}{a^n}\). So \(x^3\) can be rewritten as \(\frac{1}{x^{-3}}\).
