Solution - Simplification or other simple results

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

Equation at the end of step  1  :

  ((23) • (-3-4)) • 24

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(-4) is equal to 1/x(4) 


 2.2   Negative number raised to an even power is positive 

Equation at the end of step  2  :

  ((23) • (3)(-4)) • 24

Step  3  :

Equation at the end of step  3  :

  (23 • (3)(-4)) • 24

Step  4  :

Multiplying exponents :

 4.1    2³  multiplied by  2⁴   = 2^{(3 + 4)} = 2⁷

Final result :

  128           
  ——— = 1.58025 
  81