Question

Which expression can be simplified as StartFraction 1 Over n Superscript 18 Baseline EndFraction?
(n squared) Superscript 9
(n Superscript negative 9 Baseline) Superscript negative 2
(n Superscript negative 6 Baseline) Superscript negative 3
(n Superscript negative 3) Superscript 6

Answer 1

Use the power-of-a-power rule: (n^a)^b = n^{ab}. Evaluating each:

- (n^2)^9 = n^{18}
- (n^{-9})^{-2} = n^{18}
- (n^{-6})^{-3} = n^{18}
- (n^{-3})^6 = n^{-18} = 1/n^{18}

So (n^{-3})^6 simplifies to 1/n^{18} (assuming n ≠ 0).