Answer:
[tex]n = 12[/tex]
Step-by-step explanation:
Given
[tex](p^{20})(p^{-4})^2 = p^n[/tex]
Required
What is n?
[tex](p^{20})(p^{-4})^2 = p^n[/tex]
Apply law of indices
[tex](p^{20})(p^{-4 * 2}) = p^n[/tex]
Express -4 * 2 as -8
[tex](p^{20})(p^{-8}) = p^n[/tex]
Apply law of indices
[tex]p^{20 - 8} = p^n[/tex]
[tex]p^{12} = p^n[/tex]
Cancel p on both sides
[tex]12 = n[/tex]
[tex]n = 12[/tex]
