Question

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

Explanation:

Step1: Apply exponent division rule

When dividing terms with the same base, subtract exponents: $\frac{a^m}{a^n}=a^{m-n}$
$\frac{a^2}{a^4}=a^{2-4}$

Step2: Calculate the exponent

Compute the difference of the exponents.
$a^{2-4}=a^{-2}$

Step3: Rewrite with positive exponent

Use the rule $a^{-k}=\frac{1}{a^k}$ to rewrite the term.
$a^{-2}=\frac{1}{a^2}$

Answer:

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