Question

simplify.
\\(\frac{8x^2}{48x^6}\\)

Explanation:

Step1: Simplify the coefficients

Simplify the fraction of the coefficients \( \frac{8}{48} \). We can divide both the numerator and the denominator by their greatest common divisor, which is 8. So \( \frac{8\div8}{48\div8}=\frac{1}{6} \).

Step2: Simplify the variables

For the variable part \( \frac{x^{2}}{x^{6}} \), we use the rule of exponents \( \frac{a^{m}}{a^{n}} = a^{m - n} \) (where \( a
eq0 \)). Here, \( m = 2 \) and \( n = 6 \), so \( x^{2-6}=x^{-4} \), and \( x^{-4}=\frac{1}{x^{4}} \) (by the definition of negative exponents \( a^{-n}=\frac{1}{a^{n}} \)).

Step3: Combine the results

Multiply the simplified coefficient and the simplified variable part. So \( \frac{1}{6}\times\frac{1}{x^{4}}=\frac{1}{6x^{4}} \).

Answer:

\( \frac{1}{6x^{4}} \)