Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "1.25" was replaced by "(125/100)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

  125
  ——— • ((2)(-2)•(5)(-2))
  100

Step  2  :

            5
 Simplify   —
            4

Equation at the end of step  2  :

  5
  — • ((2)(-2)•(5)(-2))
  4

Step  3  :

Multiplying exponents :

 3.1    2²  multiplied by  2²   = 2^{(2 + 2)} = 2⁴

Dividing exponents :

 3.2    5¹   divided by   5²   = 5^{(1 - 2)} = 5^(-1) = ¹/_5¹ = ¹/₅

Final result :

   1           
  —— = 0.01250 
  80