Solution - Power equations

Step  1  :

            8
 Simplify   —
            5

Equation at the end of step  1  :

         5      8
  ((0 -  —)2) • —
         2      5

Step  2  :

            5
 Simplify   —
            2

Equation at the end of step  2  :

         5      8
  ((0 -  —)2) • —
         2      5

Step  3  :

 3.1   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  3  :

  52   8
  —— • —
  22   5

Step  4  :

Dividing exponents :

 4.1    5²   divided by   5¹   = 5^{(2 - 1)} = 5¹ = 5

Dividing exponents :

 4.2    2³   divided by   2²   = 2^{(3 - 2)} = 2¹ = 2

Final result :

  10