Solution:

Given, P = x1/3 x -1/3

To find: 3p3 – 9p

Let's simplify the given expression step by step:

Step 1: Simplifying P

P = x1/3 x -1/3
P = x(1/3 - 1/3)
P = x0
P = 1

Step 2: Substitute P in 3p3 – 9p

3p3 – 9p = 3(1)3 – 9(1)
= 3 – 9
= -6

Therefore, the value of 3p3 – 9p is -6.

Explanation:

- The given expression P is a product of two terms, x1/3 and x-1/3.
- Using the laws of exponents, we can simplify this expression to x(1/3 - 1/3) = x0 = 1.
- Hence, P is equal to 1.
- To find 3p3 – 9p, we substitute P = 1 in the expression and simplify it algebraically.
- Finally, we get the value of 3p3 – 9p as -6.

Conclusion:

- In this question, we were given an expression P and were asked to find the value of 3p3 – 9p.
- We simplified the expression P using the laws of exponents and got the value of P as 1.
- We then substituted P = 1 in the expression for 3p3 – 9p and simplified it algebraically to get the final answer of -6.