Solution - Power equations

Step  1  :

 1.1   

Negative number raised to an odd power is negative

To show this we begin with (-7)⁵ ,a negative number raised to an odd exponent:

(-7)⁵ can be written as (-7)•(-7)•(-7)•(-7)•(-7)

Now, using the rule that says minus times minus is plus, (-7)⁵ can be written as (49)•(49)•(-7) which is a negative number. 

 We showed that (-7)⁵ is a negative number  

 Using the same arguments as above, replacing (-7) by any negative number, and replacing the exponent 5 by any odd exponent, we proved which had to be proved  

  1.2     27 = 3³ (-27)⁵ = (3³)⁵ = -3¹⁵

Equation at the end of step  1  :

Step  2  :

            -315
 Simplify   ————
             3  

Dividing exponents :

 2.1    3¹⁵   divided by   3¹   = 3^{(15 - 1)} = 3¹⁴

Final result :

   -314