Question

Which expression is equivalent to (StartFraction 4 m n Over m Superscript negative 2 Baseline n Superscript 6 Baseline EndFraction) Superscript negative 2? Assume m not-equals 0, n not-equals 0.
StartFraction n Superscript 6 Baseline Over 16 m Superscript 8 Baseline EndFraction
StartFraction n Superscript 10 Baseline Over 16 m Superscript 6 Baseline EndFraction
StartFraction n Superscript 10 Baseline Over 8 m Superscript 8 Baseline EndFraction
StartFraction 4 m cubed Over n Superscript 8 Baseline EndFraction

Answer 1

Simplify inside first:

(4 m n) / (m^{-2} n^{6}) = 4 m^{1-(-2)} n^{1-6} = 4 m^{3} n^{-5}.

Now raise to -2:

(4 m^{3} n^{-5})^{-2} = 4^{-2} m^{-6} n^{10} = n^{10} / (16 m^{6}).

So the equivalent expression is: n^10 / (16 m^6).