Solution - Power equations

Step  1  :

            (100 - 6x)2
 Simplify   ———————————
                42     

Step  2  :

Pulling out like terms :

 2.1    Simplify ( 100-6x )²

Put the exponent aside and simplfy the base by pulling out like factors :
 100-6x  =  -2 • (3x-50) 

Remember the 4th law of exponents : (a • b)^m= a^m• b^m

Retract the exponent and apply the 4th law to the simplified base: ( -2 • (3x-50) )² =  (-2)² • (3x-50)²  

Dividing exponents :

 2.2    2²   divided by   2¹   = 2^{(2 - 1)} = 2¹ = 2

Equation at the end of step  2  :

  -2 • (3x - 50)2
  ——————————————— • x2
        21       

Step  3  :

Final result :

  -2x2 • (3x - 50)2
  —————————————————
         21