Question

Finding Equivalent Expressions
Which expressions can be simplified as StartFraction 1 Over p Superscript 16 EndFraction? Check all that apply.
(p-4)4
(p8)-2
(p0)-16
(p16)-1
(p-2)-8

Answer 1

Assuming the notation (p-4)4 means (p^-4)^4, etc., use the rule (a^m)^n = a^{m·n}.

- (p^-4)^4 = p^{-16} = 1/p^{16} ✓
- (p^8)^{-2} = p^{8·(-2)} = p^{-16} = 1/p^{16} ✓
- (p^0)^{-16} = p^{0·(-16)} = p^0 = 1 ✗
- (p^{16})^{-1} = p^{-16} = 1/p^{16} ✓
- (p^{-2})^{-8} = p^{(-2)·(-8)} = p^{16} (not reciprocal) ✗

So the expressions that equal 1/p^{16} are: (p^-4)^4, (p^8)^{-2}, and (p^{16})^{-1}.