Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-9" was replaced by "^(-9)".

(2): "1.2" was replaced by "(12/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)^-9 = (2•5)^(-9) = (2)^(-9) • (5)^(-9)

Equation at the end of step  1  :

    8365        12
  ((————•(103))•——)•((2)(-9)•(5)(-9))
    1000        10

Step  2  :

            6
 Simplify   —
            5

Equation at the end of step  2  :

    8365            6
  ((———— • (103)) • —) • ((2)(-9)•(5)(-9))
    1000            5

Step  3  :

 3.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  3  :

    8365              6
  ((———— • (23•53)) • —) • ((2)(-9)•(5)(-9))
    1000              5

Step  4  :

            1673
 Simplify   ————
            200 

Equation at the end of step  4  :

    1673              6
  ((———— • (23•53)) • —) • ((2)(-9)•(5)(-9))
    200               5

Step  5  :

Canceling Out :

 5.1      Canceling out  2³ as it appears on both sides of the fraction line

Dividing exponents :

 5.2    5³   divided by   5²   = 5^{(3 - 2)} = 5¹ = 5

Equation at the end of step  5  :

          6
  (8365 • —) • ((2)(-9)•(5)(-9))
          5

Step  6  :

Dividing exponents :

 6.1    2¹   divided by   2⁹   = 2^{(1 - 9)} = 2^(-8) = ¹/_2⁸

Final result :

    5019            
  ——————— = 0.00001 
  (28•59)