Basically to solve this question, simply find 2 numbers that will multiply to give you 162, in this case it would be for instance, 27 and 6. Knowing that 27 is nothing but 9 • 3, and 6 is nothing but 3 • 2, you can then rewrite cube root 162 p^8 as cube root ( 9 • 3 • 3 • 2) p^8 this can be simplified further to ( 3 • 3 • 3 • 3 • 2 • p^8), take out 3 number 3's out as in cube root unlike square root you are taking 3 numbers that are the same out, do the same for the variable, so the maximum number of p's we can take out would be 6 p's and thus have 2 p's outside the radical. ( 3 p's for every 1 p outside).
The end result would be 3 • p • p cube root 3 • 2 • p^2.
3p^2 cube root 6p^2.