Solution - Simplification or other simple results

Step  1  :

            2
 Simplify   —
            1

Equation at the end of step  1  :

  (7 +  (-42)) +  (3 • 2)

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

 2.2     4 = 2² (-4)² = (2²)² = 2⁴

Equation at the end of step  2  :

  (7 +  24) +  6

Step  3  :

Final result :

  29