(3x^3y^4)(2x^2y^6)
= 3 * x^3 * y^4 * 2 * x^2 * y^6
= 3 * 2 * color(blue)( x^3 * x^2) * color(green)( y^4 * y^6
= 6 * color(blue)( x^3 * x^2) * color(green)( y^4 * y^6
As per property:
color(blue)(a^m * a^n = a^(m+n) , applying the above to exponents of x and y.
= 6 * color(blue)( x^(3 +2)) * color(green)( y^(4 +6)
= 6 * color(blue)( x^5 * color(green)( y^10
= 6 color(blue)( x^5 color(green)( y^10