Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-3" was replaced by "^(-3)".

(2): "5.5" was replaced by "(55/10)". 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  :

   66        55
  (——•(10-3))——•(25•55))
   10(       10

Step  2  :

            11
 Simplify   ——
            2 

Equation at the end of step  2  :

   66              11
  (—— • (10-3)) ÷ (—— • (25•55))
   10              2 

Step  3  :

Raising to a Power :

 3.1    2⁵   divided by   2¹   = 2^{(5 - 1)} = 2⁴

Equation at the end of step  3  :

   66
  (—— • (10-3)) ÷ (11•24•55)
   10

Step  4  :

 4.1     10 = 2•5

(10)^-3 = (2•5)^(-3) = (2)^(-3) • (5)^(-3)

Equation at the end of step  4  :

   66
  (—— • ((2)(-3)•(5)(-3))) ÷ (11•24•55)
   10

Step  5  :

            33
 Simplify   ——
            5 

Equation at the end of step  5  :

  33
  —— • ((2)(-3)•(5)(-3))) ÷ (11•24•55)
  5 

Step  6  :

Multiplying exponents :

 6.1    5¹  multiplied by  5³   = 5^{(1 + 3)} = 5⁴

Equation at the end of step  6  :

   33 
  ———— ÷ (11•24•55)
  5000

Step  7  :

          33       
 Divide  ————  by  (11•24•55)
         5000      

Multiplying exponents :

 7.1    2³  multiplied by  2⁴   = 2^{(3 + 4)} = 2⁷

Multiplying exponents :

 7.2    5⁴  multiplied by  5⁵   = 5^{(4 + 5)} = 5⁹

Canceling Out :

 7.3      Canceling out  11  as it appears on both sides of the fraction line

Final result :

     3                                     
  ——————— = 1.20000 • 10-8 
  (27•59)