Solution - Power equations

Step  1  :

 1.1   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  1  :

Step  2  :

            -3
 Simplify   ——
            32

Dividing exponents :

 2.1    3¹   divided by   3²   = 3^{(1 - 2)} = 3^(-1) = ¹/_3¹ = ¹/₃

Final result :

  -1            
  —— = -0.33333 
  3