which expression is equivalent to $(4x^{3}y^{5})(3x^{5}y)^{2}$?\n$24x^{13}y^{7}$\n$36x^{13}y^{7}$\n$36x^{28}y…

Explanation:

Step1: Expand ((3x^{5}y)^{2})

Using the power - of - a - product rule ((ab)^n=a^n b^n) and power - of - a - power rule ((a^m)^n=a^{mn}), we have ((3x^{5}y)^{2}=3^{2}(x^{5})^{2}y^{2}=9x^{10}y^{2}).

Step2: Multiply ((4x^{3}y^{5})) and (9x^{10}y^{2})

Using the product rule (a^m\times a^n=a^{m + n}) for the same base, we get ((4x^{3}y^{5})\times(9x^{10}y^{2})=(4\times9)x^{3 + 10}y^{5+2}=36x^{13}y^{7}).

Answer:

(36x^{13}y^{7}) (corresponding to the second option)