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     10 = 2•5

(10)^-4 = (2•5)^(-4) = (2)^(-4) • (5)^(-4)

Equation at the end of step  1  :

  (5 • (102)) • (7 • ((2)(-4)•(5)(-4)))

Step  2  :

Equation at the end of step  2  :

                   7   
  (5 • (102)) • ———————
                (24•54)

Step  3  :

 3.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  3  :

                     7   
  (5 • (22•52)) • ———————
                  (24•54)

Step  4  :

Multiplying exponents :

 4.1    5¹  multiplied by  5²   = 5^{(1 + 2)} = 5³

Equation at the end of step  4  :

               7   
  (53•22) • ———————
            (24•54)

Step  5  :

Dividing exponents :

 5.1    5³   divided by   5⁴   = 5^{(3 - 4)} = 5^(-1) = ¹/_5¹ = ¹/₅

Dividing exponents :

 5.2    2²   divided by   2⁴   = 2^{(2 - 4)} = 2^(-2) = ¹/_2²

Final result :

   7           
  —— = 0.35000 
  20