Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "4." was replaced by "(4/1)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   4
  (— • (104)) • (7 • ((2)(-2)•(5)(-2)))
   1

Step  2  :

Equation at the end of step  2  :

   4             7 
  (— • (104)) • ———
   1            100

Step  3  :

 3.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  3  :

   4               7 
  (— • (24•54)) • ———
   1              100

Step  4  :

            4
 Simplify   —
            1

Equation at the end of step  4  :

                   7 
  (4 • (24•54)) • ———
                  100

Step  5  :

Multiplying exponents :

 5.1    2²  multiplied by  2⁴   = 2^{(2 + 4)} = 2⁶

Equation at the end of step  5  :

             7 
  (26•54) • ———
            100

Step  6  :

Dividing exponents :

 6.1    2⁶   divided by   2²   = 2^{(6 - 2)} = 2⁴

Dividing exponents :

 6.2    5⁴   divided by   5²   = 5^{(4 - 2)} = 5²

Final result :

  2800