Question

1. $x^{3}y^{4} \cdot 4x^{3}y^{2} \cdot -3xy^{4}$

Explanation:

Step1: Multiply the coefficients

Multiply the numerical coefficients: \(4\times(-3)= -12\)

Step2: Multiply the \(x\)-terms

Use the rule \(a^m \cdot a^n = a^{m + n}\) for \(x\)-terms: \(x^3\cdot x^3\cdot x = x^{3 + 3 + 1}=x^7\)

Step3: Multiply the \(y\)-terms

Use the same exponent rule for \(y\)-terms: \(y^4\cdot y^2\cdot y^4 = y^{4 + 2 + 4}=y^{10}\)

Step4: Combine all parts

Multiply the coefficient, \(x\)-term, and \(y\)-term together: \(-12\times x^7\times y^{10}=-12x^7y^{10}\)

Answer:

\(-12x^7y^{10}\)