Question

simplify \\(\frac{42x^2y}{15} \cdot \frac{5y^2}{7x^3}\\).

Explanation:

Step1: Multiply numerators and denominators

Multiply the numerators \(42x^{2}y\) and \(5y^{2}\), and denominators \(15\) and \(7x^{3}\). So we get \(\frac{42x^{2}y\times5y^{2}}{15\times7x^{3}}\).

Step2: Simplify coefficients and variables

Simplify the coefficients: \(42\times5 = 210\), \(15\times7=105\), so \(\frac{210}{105} = 2\). For variables, \(x^{2}\div x^{3}=x^{2 - 3}=x^{-1}=\frac{1}{x}\), \(y\times y^{2}=y^{1 + 2}=y^{3}\). Then multiply the simplified parts: \(2\times\frac{y^{3}}{x}=\frac{2y^{3}}{x}\).

Answer:

\(\frac{2y^{3}}{x}\)