Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "0.05" was replaced by "(05/100)".

Step  1  :

             1
 Simplify   ——
            20

Equation at the end of step  1  :

  )1 
 (———)2)
  (20

Step  2  :

 2.1     20 = 2²•5 (20)² = (2²•5)² = 2⁴ • 5²

Equation at the end of step  2  :

  6))1 
  ———————
  (24•52)

Step  3  :

 3.1     10 = 2•5

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

Equation at the end of step  3  :

  )))1 
  ———————
  (24•52)

Step  4  :

Dividing exponents :

 4.1    2¹   divided by   2⁶   = 2^{(1 - 6)} = 2^(-5) = ¹/_2⁵

Dividing exponents :

 4.2    5¹   divided by   5⁶   = 5^{(1 - 6)} = 5^(-5) = ¹/_5⁵

Equation at the end of step  4  :

     3         1   
  ——————— ÷ ———————
  (25•55)   (24•52)

Step  5  :

            3            1   
 Divide  ———————  by  ———————
         (25•55)      (24•52)

 5.1    Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

   3           1             3        (24•52)
———————  ÷  ———————   =   ———————  •  ———————
(25•55)     (24•52)       (25•55)        1   

Dividing exponents :

 5.2    2⁴   divided by   2⁵   = 2^{(4 - 5)} = 2^(-1) = ¹/_2¹ = ¹/₂

Dividing exponents :

 5.3    5²   divided by   5⁵   = 5^{(2 - 5)} = 5^(-3) = ¹/_5³

Final result :

   3            
  ——— = 0.01200 
  250