Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-2" was replaced by "^(-2)".

(2): "1.51" was replaced by "(151/100)".

Step  1  :

 1.1   

Negative number raised to an odd power is negative

To show this we begin with (-7)⁵ ,a negative number raised to an odd exponent:

(-7)⁵ can be written as (-7)•(-7)•(-7)•(-7)•(-7)

Now, using the rule that says minus times minus is plus, (-7)⁵ can be written as (49)•(49)•(-7) which is a negative number. 

 We showed that (-7)⁵ is a negative number  

 Using the same arguments as above, replacing (-7) by any negative number, and replacing the exponent 5 by any odd exponent, we proved which had to be proved  

 

Equation at the end of step  1  :

   151
  {———}-2^3
   100

Step  2  :

            151
 Simplify   ———
            100

Equation at the end of step  2  :

  151
 (———)-2^3
  100

Step  3  :

 3.1     100 = 2²•5² (100)^-8 = (2²•5²)^(-8) = (2)^(-16) • (5)^(-16)

Final result :

  1 • (216•516) 
  —————————————
    1 • 1518