Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-2" was replaced by "^(-2)".

Step  1  :

 1.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  1  :

       (10-2)
  (5 • ——————) • (25•55)
         2   

Step  2  :

 2.1     10 = 2•5

(10)^-2 = (2•5)^(-2) = (2)^(-2) • (5)^(-2)

Equation at the end of step  2  :

       ((2)(-2)•(5)(-2)) 
  (5 • —————————————————) • (25•55)
               2        

Step  3  :

            1         
 Divide  ———————  by  2
         (22•52)      

Multiplying exponents :

 3.1    2²  multiplied by  2¹   = 2^{(2 + 1)} = 2³

Equation at the end of step  3  :

        1 
  (5 • ———) • (25•55)
       200

Step  4  :

Dividing exponents :

 4.1    2⁵   divided by   2³   = 2^{(5 - 3)} = 2²

Dividing exponents :

 4.2    5⁵   divided by   5¹   = 5^{(5 - 1)} = 5⁴

Final result :

  2500