Question

1. \\(\frac{4x^2}{2x^4}\\)

Explanation:

Step1: Simplify the coefficient

Simplify the fraction of the coefficients \( \frac{4}{2} \).
\( \frac{4}{2} = 2 \)

Step2: Simplify the variable part

Use the rule of exponents \( \frac{x^m}{x^n}=x^{m - n} \) for the variable \( x \), where \( m = 2 \) and \( n = 4 \).
\( \frac{x^2}{x^4}=x^{2 - 4}=x^{-2}=\frac{1}{x^2} \) (using the rule \( x^{-n}=\frac{1}{x^n} \))

Step3: Combine the results

Multiply the simplified coefficient and the simplified variable part.
\( 2\times\frac{1}{x^2}=\frac{2}{x^2} \)

Answer:

\( \frac{2}{x^2} \)