Solution - Simplification or other simple results

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  

 

Equation at the end of step  1  :

  ((25) • (-3-3)) •  -23

Step  2  :

 2.1   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(-3) is equal to 1/x(3) 


 2.2   

Negative number raised to an odd power is negative

Equation at the end of step  2  :

  ((25) •  -(3)(-3)) •  -23

Step  3  :

Equation at the end of step  3  :

  (25 •  -(3)(-3)) •  -23

Step  4  :

Multiplying exponents :

 4.1    2⁵  multiplied by  2³   = 2^{(5 + 3)} = 2⁸

Final result :

  256           
  ——— = 9.48148 
  27