Solution - Power equations

Step  1  :

Equation at the end of step  1  :

  ((-33) • (62)) • (3)(-2)

Step  2  :

 2.1     6 = 2•3

(6)² = (2•3)² = 2² • 3²

Equation at the end of step  2  :

  ((-33) • (22•32)) • (3)(-2)

Step  3  :

 3.1   

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  

 

Equation at the end of step  3  :

  ( -33 • (22•32)) • (3)(-2)
 Step  4  :

Dividing exponents :

 4.1    3⁵   divided by   3²   = 3^{(5 - 2)} = 3³

Final result :

  -108