which term is a perfect square of the root 3x^4?\n6x^8\n6x^16\n9x^8\n9x^16

Explanation:

Step1: Recall the power - of - a - product rule

The power - of - a - product rule states that ((ab)^n=a^n\times b^n). Here, if we have ((3x^{4})^2), we can expand it as (3^2\times(x^{4})^2).

Step2: Calculate (3^2)

(3^2 = 9).

Step3: Calculate ((x^{4})^2)

According to the power - of - a - power rule ((a^m)^n=a^{mn}), so ((x^{4})^2=x^{4\times2}=x^{8}).

Step4: Combine the results

((3x^{4})^2=3^2\times(x^{4})^2 = 9x^{8}).

Answer:

C. (9x^{8})