simplify. \n\\frac{a^{2}}{a^{4}}

Explanation:

Step1: Use the quotient rule of exponents

The quotient rule states that $\frac{a^m}{a^n}=a^{m - n}$. Here, $m = 2$ and $n = 4$. $$\frac{a^2}{a^4}=a^{2-4}$$

Step2: Simplify the exponent

Calculate $2 - 4=-2$. $$a^{2 - 4}=a^{-2}$$

Step3: Rewrite using positive exponent

Using the rule $a^{-n}=\frac{1}{a^n}$, we get $a^{-2}=\frac{1}{a^2}$.

Answer:

$\frac{1}{a^2}$