Answer Happy

Hi! It factored out the "-3/2" exponent, leaving the binomial to the 1st power; yet, that 1st power binomial is a product with "a" or should it not be? However, the solution separates it from "a" with the brackets, and thus permits everything within the brackets to become "1". (I need help only with the factoring/algebra, I placed a red pen cap in the pic to demonstrate exactly where) Thanks!
Pic 1(originalquestion for your reference):
Pic 2 (Solutions manual):
Pic 3 (my understanding of how I think it should appear ):
23. The force F acting on a body with mass m and velocity v is the rate of change of momentum: F = (d/dt) (mv). If m is constant, this becomes F = ma, where a = dv/dt is the acceleration. But in the theory of relativity, the mass of a particle varies with v as follows: m = mo/√1-v²/c² where mo is the mass of the particle at rest and c is the speed of light. Show that F = moa (1 - v²/c²)3/2
23. With m=mo 1- = d -1/2 F-(+)-(1-5)+(-)"](-) » 2,2 -1/2 mo (1-²) dt m v d (m): =mo -3/2 = mo (1-5)-¹² · [(¹-²) + =] =(1-12/27/2 moa a -3/27 2v Note that we factore 1-v²/c²)-3/2 since -3/2 was the lesser exponent. Also note that (v) = = a.
2 ई 12 141 N -3/2 -312 oR - 2 6 उ + V 2 ऋतु