Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-4" was replaced by "^(-4)".

Step  1  :

 1.1   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) 


 1.2   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  :

  0 -  (7 • (7)(-4))

Step  2  :

Dividing exponents :

 2.1    7¹   divided by   7⁴   = 7^{(1 - 4)} = 7^(-3) = ¹/_7³

Equation at the end of step  2  :

        1 
  0 -  ———
       343

Step  3  :

Final result :

   -1            
  ——— = -0.00292 
  343