Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-6" was replaced by "^(-6)".

(2): "3.8" was replaced by "(38/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)^-6 = (2•5)^(-6) = (2)^(-6) • (5)^(-6)

Equation at the end of step  1  :

   24         38
  (——•(104))•(——•((2)(-6)•(5)(-6)))
   10         10

Step  2  :

            19
 Simplify   ——
            5 

Equation at the end of step  2  :

   24             19
  (—— • (104)) • (—— • ((2)(-6)•(5)(-6)))
   10             5 

Step  3  :

Raising to a Power :

 3.1    5¹  multiplied by  5⁶   = 5^{(1 + 6)} = 5⁷

Equation at the end of step  3  :

   24               19  
  (—— • (104)) • ———————
   10            (57•26)

Step  4  :

 4.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  4  :

   24                 19  
  (—— • (24•54)) • ———————
   10              (57•26)

Step  5  :

            12
 Simplify   ——
            5 

Equation at the end of step  5  :

   12                 19  
  (—— • (24•54)) • ———————
   5               (57•26)

Step  6  :

Multiplying exponents :

 6.1    2²  multiplied by  2⁴   = 2^{(2 + 4)} = 2⁶

Dividing exponents :

 6.2    5⁴   divided by   5¹   = 5^{(4 - 1)} = 5³

Equation at the end of step  6  :

                 19  
  (26•3•53) • ———————
              (57•26)

Step  7  :

Canceling Out :

 7.1      Canceling out  2⁶ as it appears on both sides of the fraction line

Dividing exponents :

 7.2    5³   divided by   5⁷   = 5^{(3 - 7)} = 5^(-4) = ¹/_5⁴

Final result :

   57           
  ——— = 0.09120 
  625