Question

in the pic....................Complete the puzzle by selecting the puzzle piece that contains equivalent expression.

Answer 1

`\begin{gathered} \text{Given} \\ ((2x^2y^3)^5)/((4x^4y)(y^(12))) \end{gathered}`

Simplifying the given expression, we have the following:

`\begin{gathered} ((2x^2y^3)^5)/((4x^4y)(y^(12))) \\ =(2^5x^(2\cdot5)y^(3\cdot5))/(4x^4y^(1+12)) \\ =(32x^(10)y^(15))/(4x^4y^(13)) \end{gathered}`

Reducing the fraction to its lowest term we get

`\begin{gathered} (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} \\ ((2x^2y^3)^5)/((4x^4y)(y^(12)))=8x^6y^(12) \end{gathered}`