Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

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

Step  1  :

             64
 Simplify   ———
            125

Equation at the end of step  1  :

   64
  ———)-1) ÷ 3
  125

Step  2  :

 2.1   Raising to a negative exponent

Raising a number to a negative exponent means 1 over that 
same number but now with a positive exponent.

For example, x(-1) is equal to 1/x(1) 


 2.2   

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  

  2.3     64 = 2⁶ (-64)^-1 = (2⁶)^(-1) = (2)^(-6)  2.4     125 = 5³ (125)^-1 = (5³)^(-1) = (5)^(-3)

Equation at the end of step  2  :

  -(2)(-6)
  ———————— ÷ 3
  (5)(-3) 

Step  3  :

         -(2)(-6)      
 Divide  ————————  by  3
         (5)(-3)       

Final result :

  -125            
  ———— = -0.65104 
  192