Question

1. \\(\frac{10x^{-2}y^{7}}{20x^{3}y}\\)

Explanation:

Step1: Simplify coefficients

Simplify \(\frac{10}{20}\) to \(\frac{1}{2}\).

Step2: Simplify \(x\)-terms

Using the rule \(a^m\div a^n = a^{m - n}\), for \(x\)-terms: \(x^{-2}\div x^{3}=x^{-2 - 3}=x^{-5}=\frac{1}{x^{5}}\).

Step3: Simplify \(y\)-terms

For \(y\)-terms: \(y^{7}\div y^{1}=y^{7 - 1}=y^{6}\).

Step4: Combine all parts

Multiply the simplified coefficient, \(x\)-term, and \(y\)-term: \(\frac{1}{2}\times\frac{1}{x^{5}}\times y^{6}=\frac{y^{6}}{2x^{5}}\).

Answer:

\(\boldsymbol{\frac{y^{6}}{2x^{5}}}\)