Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-45" was replaced by "^(-45)". 1 more similar replacement(s)

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

 1.2     45 = 3²•5 (-45)⁴ = (3²•5)⁴ = 3⁸ • 5⁴

Equation at the end of step  1  :

Step  2  :

 2.1     4 = 22

(4)^4100625 = (2²)^4100625 = 2^8201250

Equation at the end of step  2  :

Step  3  :

 3.1   Negative number raised to an even power is positive 

 3.2     25 = 52

(-25)² = (5²)² = 5⁴

Equation at the end of step  3  :

Step  4  :

Equation at the end of step  4  :

Step  5  :

              2625  
 Simplify   ————————
            28201250 

Dividing exponents :

 5.1    2⁶²⁵   divided by   2^8201250   = 2^{(625 - 8201250)} = 2^(-8200625) = ¹/_2^8200625

Final result :

      1                                           
  ———————— = 7.79486 • 10-2468635 
  28200625