Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-12" was replaced by "^(-12)". 1 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)^-12 = (2•5)^(-12) = (2)^(-12) • (5)^(-12)

Equation at the end of step  1  :

Step  2  :

Raising to a Power :

 2.1    5¹   divided by   5¹²   = 5^{(1 - 12)} = 5^(-11) = ¹/_5¹¹

Equation at the end of step  2  :

  14))1 
  —————————
  (212•511) 

Step  3  :

 3.1     10 = 2•5

(10)^-14 = (2•5)^(-14) = (2)^(-14) • (5)^(-14)

Equation at the end of step  3  :

  4)))1 
  —————————
  (212•511) 

Step  4  :

             1              1    
 Divide  —————————  by  —————————
         (214•514)       (212•511) 

 4.1    Dividing fractions

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

    1             1               1         (212•511) 
—————————  ÷  —————————   =   —————————  •  —————————
(214•514)      (212•511)        (214•514)          1    

Dividing exponents :

 4.2    2¹²   divided by   2¹⁴   = 2^{(12 - 14)} = 2^(-2) = ¹/_2²

Dividing exponents :

 4.3    5¹¹   divided by   5¹⁴   = 5^{(11 - 14)} = 5^(-3) = ¹/_5³

Final result :

   1            
  ——— = 0.00200 
  500