Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.05" was replaced by "(105/100)".

Step  1  :

            21
 Simplify   ——
            20

Equation at the end of step  1  :

           21
  30000 • (——)21)
           20

Step  2  :

 2.1     21 = 3•7

(21)²¹ = (3•7)²¹ = 3²¹ • 7²¹  2.2     20 = 2²•5 (20)²¹ = (2²•5)²¹ = 2⁴² • 5²¹

Equation at the end of step  2  :

          (321•721)
  30000 • —————————
          (242•521)

Step  3  :

Multiplying exponents :

 3.1    3¹  multiplied by  3²¹   = 3^{(1 + 21)} = 3²²

Dividing exponents :

 3.2    2⁴   divided by   2⁴²   = 2^{(4 - 42)} = 2^(-38) = ¹/_2³⁸

Dividing exponents :

 3.3    5⁴   divided by   5²¹   = 5^{(4 - 21)} = 5^(-17) = ¹/_5¹⁷

Final result :

  (322•721)               
  ————————— = 83578.87771 
  (238•517)