We are given the following function:
![p(x)=3x^2-4](https://img.qammunity.org/2023/formulas/mathematics/high-school/1af90s79h7cppi3tqesurafccyh92q86la.png)
We are asked to determine the value of p(8a). That means that we will substitute the value of "x = 8a" in the function, like this:
![p(8a)=3(8a)^2-4](https://img.qammunity.org/2023/formulas/mathematics/high-school/b9gcjs7cgytnsvdgqg2ak9pysbwspabmmg.png)
Now, we solve the exponents using the following property:
![(ab)^x=a^xb^x](https://img.qammunity.org/2023/formulas/mathematics/high-school/eamyr4sfjremhu7qyizks5drr6tqaocw9e.png)
Applying the property we get:
![p(8a)=3(8^2a^2)-4](https://img.qammunity.org/2023/formulas/mathematics/high-school/un8c5vwxfvvekj8pejzk6zxg4ci7tttqnv.png)
Solving the products we get:
![p(8a)=192a^2-4](https://img.qammunity.org/2023/formulas/mathematics/high-school/wx1u2v167cj50nhg7cr9x3oouekulhgqol.png)
Since we can't simplify any further this is the final answer.