Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "1.95" was replaced by "(195/100)". 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  :

   408         195
  (———•(102))•(———•((2)(-6)•(5)(-6)))
   100         100

Step  2  :

            39
 Simplify   ——
            20

Equation at the end of step  2  :

   408             39
  (——— • (102)) • (—— • ((2)(-6)•(5)(-6)))
   100             20

Step  3  :

Multiplying exponents :

 3.1    2²  multiplied by  2⁶   = 2^{(2 + 6)} = 2⁸

Raising to a Power :

 3.2    5¹  multiplied by  5⁶   = 5^{(1 + 6)} = 5⁷

Equation at the end of step  3  :

   408               39  
  (——— • (102)) • ———————
   100            (28•57)

Step  4  :

 4.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  4  :

   408                 39  
  (——— • (22•52)) • ———————
   100              (28•57)

Step  5  :

            102
 Simplify   ———
            25 

Equation at the end of step  5  :

   102                 39  
  (——— • (22•52)) • ———————
   25               (28•57)

Step  6  :

Multiplying exponents :

 6.1    2¹  multiplied by  2²   = 2^{(1 + 2)} = 2³

Canceling Out :

 6.2      Canceling out  5² as it appears on both sides of the fraction line

Equation at the end of step  6  :

           39  
  408 • ———————
        (28•57)

Step  7  :

Dividing exponents :

 7.1    2³   divided by   2⁸   = 2^{(3 - 8)} = 2^(-5) = ¹/_2⁵

Final result :

    1989            
  ——————— = 0.00080 
  (25•57)