Answer: The correct option is (C)
![a^5.](https://img.qammunity.org/2020/formulas/mathematics/middle-school/vlor41sbkt0dz9zz028q658m330s7cuz0r.png)
Step-by-step explanation: We are given to choose the correct simplification for the following expression :
![P=a^2.a^3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/155n0gbgeuflea9b77nz627n7j1rhpcdjb.png)
We will be using the following property of exponents :
![x^a.x^b=x^(a+b).](https://img.qammunity.org/2020/formulas/mathematics/middle-school/nkhjemcwyp67rclpexyksvhbdcd0rmzlsh.png)
So, the simplification of expression (i) is as follows :
![P\\\\=a^2.a^3\\\\=a^(2+3)\\\\=a^5.](https://img.qammunity.org/2020/formulas/mathematics/middle-school/zjh3qzhdro1barglj8y8kfvg7iq9p31en2.png)
Thus, the correct simplification of the given expression is
![a^5.](https://img.qammunity.org/2020/formulas/mathematics/middle-school/vlor41sbkt0dz9zz028q658m330s7cuz0r.png)
Option (C) is CORRECT.