[tex]\begin{gathered} \text{Given} \\ \frac{(2x^2y^3)^5}{(4x^4y)(y^{12})} \end{gathered}[/tex]
Simplifying the given expression, we have the following:
[tex]\begin{gathered} \frac{(2x^2y^3)^5}{(4x^4y)(y^{12})} \\ =\frac{2^5x^{2\cdot5}y^{3\cdot5}}{4x^4y^{1+12}} \\ =\frac{32x^{10}y^{15}}{4x^4y^{13}} \end{gathered}[/tex]
Reducing the fraction to its lowest term we get
[tex]\begin{gathered} \frac{32x^{10}y^{15}}{4x^4y^{13}} \\ =8x^{10-4}y^{15-3} \\ =8x^6y^{12} \\ \\ \text{Therefore, the equivalent expression of the given is} \\ \frac{(2x^2y^3)^5}{(4x^4y)(y^{12})}=8x^6y^{12} \end{gathered}[/tex]
