Question

(\frac{t^{-4}t^{2}}{t^{2}}=)

Explanation:

Step1: Simplify numerator (exponent rule)

Using the rule \(a^m \cdot a^n = a^{m + n}\), for \(t^{-4} \cdot t^2\), we have \(m=-4\) and \(n = 2\). So \(t^{-4+2}=t^{-2}\). Now the expression becomes \(\frac{t^{-2}}{t^{2}}\).

Step2: Simplify the fraction (exponent rule)

Using the rule \(\frac{a^m}{a^n}=a^{m - n}\), here \(m=-2\) and \(n = 2\). So \(t^{-2-2}=t^{-4}\). We can also write \(t^{-4}\) as \(\frac{1}{t^{4}}\) (using \(a^{-n}=\frac{1}{a^{n}}\)).

Answer:

\(\frac{1}{t^{4}}\) (or \(t^{-4}\))