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

 1.2     27 = 3³ (-27)² = (3³)² = 3⁶

Equation at the end of step  1  :

Step  2  :

            36
 Simplify   ——
            3 

Dividing exponents :

 2.1    3⁶   divided by   3¹   = 3^{(6 - 1)} = 3⁵

Final result :

  243