Question

1. \\(\frac{3x^2y^3}{3xy^2}\\)

Explanation:

Step1: Simplify coefficients

The coefficient of the numerator is 3 and the coefficient of the denominator is 3. So, $\frac{3}{3} = 1$.

Step2: Simplify x terms

For the variable \(x\), we have \(x^3\) in the numerator and \(x\) in the denominator. Using the rule of exponents \(\frac{x^m}{x^n}=x^{m - n}\), we get \(x^{3-1}=x^2\).

Step3: Simplify y terms

For the variable \(y\), we have \(y^3\) in the numerator and \(y^2\) in the denominator. Using the rule of exponents \(\frac{y^m}{y^n}=y^{m - n}\), we get \(y^{3 - 2}=y\).

Step4: Combine the results

Multiply the results from Step1, Step2, and Step3 together. So, \(1\times x^2\times y=x^2y\).

Answer:

\(x^2y\)