Question

1. \\(\frac{9x^7y^3}{xy} \cdot \frac{2x^6y^8}{3x^3y^4}\\)

Explanation:

Step1: Multiply coefficients and variables separately

First, multiply the coefficients: \( \frac{9\times2}{1\times3} = \frac{18}{3}=6 \). Then, for the \( x \)-terms, use the rule of exponents \( a^m \cdot a^n = a^{m + n} \) and \( \frac{a^m}{a^n}=a^{m - n} \). So for \( x \): \( \frac{x^7}{x} \cdot \frac{x^6}{x^3}=x^{7 - 1+6 - 3}=x^{9} \). For \( y \)-terms: \( \frac{y^3}{y} \cdot \frac{y^8}{y^4}=y^{3 - 1+8 - 4}=y^{6} \).

Step2: Combine the results

Multiply the coefficient, \( x \)-term, and \( y \)-term together: \( 6\times x^{9}\times y^{6}=6x^{9}y^{6} \).

Answer:

\( 6x^{9}y^{6} \)