Solution - Power equations

Step  1  :

Equation at the end of step  1  :

  ((-3-5) • (2-2)) • 32

Step  2  :

Equation at the end of step  2  :

  ((-3-5) • (2)(-2)) • 32

Step  3  :

 3.1   Raising to a negative exponent

Raising a number to a negative exponent means 1 over that 
same number but now with a positive exponent.

For example, x(-5) is equal to 1/x(5) 


 3.2   

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  :

  ( -(3)(-5) • (2)(-2)) • 32

Step  4  :

Dividing exponents :

 4.1    3²   divided by   3⁵   = 3^{(2 - 5)} = 3^(-3) = ¹/_3³

Final result :

   -1            
  ——— = -0.00926 
  108