Question

(\frac{3x^{3}y^{4}}{18x^{2}y^{6}})

Explanation:

Step1: Simplify the coefficient

Divide the coefficient 3 by 18. So, $\frac{3}{18}=\frac{1}{6}$.

Step2: Simplify the \(x\)-term

Using the rule of exponents \( \frac{x^m}{x^n}=x^{m - n} \), for \(x\) terms we have \( \frac{x^3}{x^2}=x^{3 - 2}=x^1 = x \).

Step3: Simplify the \(y\)-term

Using the same exponent rule, for \(y\) terms we have \( \frac{y^4}{y^6}=y^{4 - 6}=y^{-2}=\frac{1}{y^2} \) (since \(a^{-n}=\frac{1}{a^n}\)).

Step4: Combine all simplified parts

Multiply the simplified coefficient, \(x\)-term, and \(y\)-term together. So we get \( \frac{1}{6}\times x\times\frac{1}{y^2}=\frac{x}{6y^2} \).

Answer:

\(\frac{x}{6y^2}\)