Question

Which expression is equivalent to StartFraction (4 p Superscript negative 4 Baseline q) Superscript negative 2 Baseline Over 10 p q Superscript negative 3 Baseline EndFraction? Assume p not-equals 0, q not-equals 0.
StartFraction 25 p Superscript 10 Baseline Over 4 q Superscript 8 Baseline EndFraction
StartFraction 2 q Over 5 p Superscript 5 Baseline EndFraction
StartFraction p Superscript 7 Baseline q Over 160 EndFraction
StartFraction 125 p Superscript 11 Baseline q Over 2 EndFraction

Answer 1

Simplify stepwise:

(4 p⁻⁴ q)⁻² = 4⁻² · p^{8} · q⁻² = (1/16) p⁸ q⁻².

Now divide by 10 p q⁻³:
[(1/16) p⁸ q⁻²] / [10 p q⁻³] = (1/16) p⁸ q⁻² · q³/(10 p)
= p^{8-1} q^{3-2} / (16·10)
= p⁷ q / 160.

So the equivalent expression is p⁷ q / 160 (third option).