Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-9" was replaced by "^(-9)". 1 more similar replacement(s)

(2): "0.534" was replaced by "(534/1000)". 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  :

    145          534
  ((———•(10-9))•————)•((2)(-9)•(5)(-9))
    100         1000

Step  2  :

            267
 Simplify   ———
            500

Equation at the end of step  2  :

    145             267
  ((——— • (10-9)) • ———) • ((2)(-9)•(5)(-9))
    100             500

Step  3  :

 3.1     10 = 2•5

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

Equation at the end of step  3  :

    145                        267
  ((——— • ((2)(-9)•(5)(-9))) • ———) • ((2)(-9)•(5)(-9))
    100                        500

Step  4  :

            29
 Simplify   ——
            20

Equation at the end of step  4  :

    29                        267
  ((—— • ((2)(-9)•(5)(-9))) • ———) • ((2)(-9)•(5)(-9))
    20                        500

Step  5  :

Multiplying exponents :

 5.1    2²  multiplied by  2⁹   = 2^{(2 + 9)} = 2¹¹

Multiplying exponents :

 5.2    5¹  multiplied by  5⁹   = 5^{(1 + 9)} = 5¹⁰

Equation at the end of step  5  :

       29      267
  (————————— • ———) • ((2)(-9)•(5)(-9))
   (211•510)    500

Step  6  :

Multiplying exponents :

 6.1    2¹¹  multiplied by  2²   = 2^{(11 + 2)} = 2¹³

Multiplying exponents :

 6.2    5¹⁰  multiplied by  5³   = 5^{(10 + 3)} = 5¹³

Equation at the end of step  6  :

     7743  
  ————————— • ((2)(-9)•(5)(-9))
  (213•513) 

Step  7  :

Multiplying exponents :

 7.1    2¹³  multiplied by  2⁹   = 2^{(13 + 9)} = 2²²

Multiplying exponents :

 7.2    5¹³  multiplied by  5⁹   = 5^{(13 + 9)} = 5²²

Final result :

     7743                                     
  ————————— = 7.74300 • 10-19 
  (222•522)