Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "3.8" was replaced by "(38/10)".

Step  1  :

 1.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  1  :

   38
  (—— • (10-9)) • (4 • (24•54))
   10

Step  2  :

Raising to a Power :

 2.1    2²  multiplied by  2⁴   = 2^{(2 + 4)} = 2⁶

Equation at the end of step  2  :

   38
  (—— • (10-9)) • (26•54)
   10

Step  3  :

 3.1     10 = 2•5

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

Equation at the end of step  3  :

   38
  (—— • ((2)(-9)•(5)(-9))) • (26•54)
   10

Step  4  :

            19
 Simplify   ——
            5 

Equation at the end of step  4  :

   19
  (—— • ((2)(-9)•(5)(-9))) • (26•54)
   5 

Step  5  :

Multiplying exponents :

 5.1    5¹  multiplied by  5⁹   = 5^{(1 + 9)} = 5¹⁰

Equation at the end of step  5  :

     19   
  ———————— • (26•54)
  (510•29) 

Step  6  :

Dividing exponents :

 6.1    2⁶   divided by   2⁹   = 2^{(6 - 9)} = 2^(-3) = ¹/_2³

Dividing exponents :

 6.2    5⁴   divided by   5¹⁰   = 5^{(4 - 10)} = 5^(-6) = ¹/_5⁶

Final result :

     19             
  ——————— = 0.00015 
  (56•23)