Solution - Simplification or other simple results

Step  1  :

            -1
 Simplify   ——
            3 

Equation at the end of step  1  :

                               -1
  ((4 • (-22)) +  -16) +  (3 • ——)
                               3 

Step  2  :

 2.1   Negative number raised to an even power is positive 

For example let's look at (-7)⁶ , where (-7) , a negative number, is raised to 6 , an even exponent :

(-7)⁶ can be written as (-7)•(-7)•(-7)•(-7)•(-7)•(-7)

Now, using the rule that says minus times minus is plus, (-7)⁶ can be written as (49)•(49)•(49) which in turn can be written as (7)•(7)•(7)•(7)•(7)•(7) or 7⁶ which is positive.

We proved that (-7)⁶ is equal to (7)⁶ which is a positive number

Using the same arguments as above, replacing (-7) by any negative number, and replacing the exponent 6 by any even exponent, we proved which had to be proved

Equation at the end of step  2  :

  ((4 • 22) +  -16) +  -1

Step  3  :

Multiplying exponents :

 3.1    2²  multiplied by  2²   = 2^{(2 + 2)} = 2⁴

Equation at the end of step  3  :

  (24 +  -16) +  -1

Step  4  :

Final result :

  -1