Solution - Simplification or other simple results

Step  1  :

             1
 Simplify   ——
            56

Equation at the end of step  1  :

  (-75)   (1
  ————— •(——)5) ÷ 3
    3     56

Step  2  :

 2.1     56 = 2³•7 (56)⁵ = (2³•7)⁵ = 2¹⁵ • 7⁵

Equation at the end of step  2  :

  (-75)       1   
  ————— • ———————— ÷ 3
    3     (215•75) 

Step  3  :

             1         
 Divide  ————————  by  3
         (215•75)       

Equation at the end of step  3  :

  (-75)        1    
  ————— • ——————————
    3     (215•75•3) 

Step  4  :

 4.1   

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  4  :

  -75        1    
  ——— • ——————————
   3    (215•75•3) 

Step  5  :

            -75
 Simplify   ———
             3 

Equation at the end of step  5  :

  -75        1    
  ——— • ——————————
   3    (215•75•3) 

Step  6  :

Multiplying exponents :

 6.1    3¹  multiplied by  3¹   = 3^{(1 + 1)} = 3²

Canceling Out :

 6.2      Canceling out  7⁵ as it appears on both sides of the fraction line

Final result :

     -1                                      
  ———————— = -3.39084 • 10-6 
  (32•215)