Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "6.53" was replaced by "(653/100)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  1  :

    838         653
  ((———•(10-2))•———)•(25•55)
    100         100

Step  2  :

            653
 Simplify   ———
            100

Equation at the end of step  2  :

    838             653
  ((——— • (10-2)) • ———) • (25•55)
    100             100

Step  3  :

 3.1     10 = 2•5

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

Equation at the end of step  3  :

    838                        653
  ((——— • ((2)(-2)•(5)(-2))) • ———) • (25•55)
    100                        100

Step  4  :

            419
 Simplify   ———
            50 

Equation at the end of step  4  :

    419                        653
  ((——— • ((2)(-2)•(5)(-2))) • ———) • (25•55)
    50                         100

Step  5  :

Multiplying exponents :

 5.1    2¹  multiplied by  2²   = 2^{(1 + 2)} = 2³

Multiplying exponents :

 5.2    5²  multiplied by  5²   = 5^{(2 + 2)} = 5⁴

Equation at the end of step  5  :

    419   653
  (———— • ———) • (25•55)
   5000   100

Step  6  :

Canceling Out :

 6.1      Canceling out  2⁵ as it appears on both sides of the fraction line

Dividing exponents :

 6.2    5⁵   divided by   5⁶   = 5^{(5 - 6)} = 5^(-1) = ¹/_5¹ = ¹/₅

Final result :

  (419•653)               
  ————————— = 54721.40000 
      5