Question

What is the simplified form of StartRoot StartFraction 72 x Superscript 16 Baseline Over 50 x Superscript 36 Baseline EndFraction EndRoot? Assume x ≠ 0.

StartFraction 6 Over 5 x Superscript 10 Baseline EndFraction
StartFraction 6 Over 5 x squared EndFraction
Six-fifths x Superscript 10
Six-fifths x squared

Answer 1

Simplify inside the radical:
(72/50) x^(16-36) = (36/25) x^(-20).

Take square roots:
sqrt(36/25) = 6/5 and sqrt(x^(-20)) = x^(-10) = 1/x^10.

So the result is 6/(5 x^10).