Question

4)
\frac{3x^{3}y^{3}}{3xy^{2}}

Explanation:

Step1: Simplify the coefficient

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

Step2: Simplify the \(x\)-terms

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

Step3: Simplify the \(y\)-terms

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

Step4: Combine the results

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

Answer:

\(x^{2}y\)