Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-19" was replaced by "^(-19)". 1 more similar replacement(s)

(2): "1.6" was replaced by "(16/10)".

Step  1  :

 1.1     10 = 2•5

(10)^-19 = (2•5)^(-19) = (2)^(-19) • (5)^(-19)

Equation at the end of step  1  :

  )16
  ——— • ((2)(-19)•(5)(-19)))
  (10

Step  2  :

            8
 Simplify   —
            5

Equation at the end of step  2  :

  )8
  —— • ((2)(-19)•(5)(-19)))
  (5

Step  3  :

Multiplying exponents :

 3.1    5¹  multiplied by  5¹⁹   = 5^{(1 + 19)} = 5²⁰

Raising to a Power :

 3.2    2³   divided by   2¹⁹   = 2^{(3 - 19)} = 2^(-16) = ¹/_2¹⁶

Equation at the end of step  3  :

  20))1 
  —————————
  (520•216) 

Step  4  :

 4.1     10 = 2•5

(10)^-20 = (2•5)^(-20) = (2)^(-20) • (5)^(-20)

Equation at the end of step  4  :

  0)))1 
  —————————
  (520•216) 

Step  5  :

Dividing exponents :

 5.1    2³   divided by   2²⁰   = 2^{(3 - 20)} = 2^(-17) = ¹/_2¹⁷

Equation at the end of step  5  :

      1           1    
  ————————— ÷ —————————
  (217•520)    (520•216) 

Step  6  :

             1              1    
 Divide  —————————  by  —————————
         (217•520)       (520•216) 

 6.1    Dividing fractions

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

    1             1               1         (520•216) 
—————————  ÷  —————————   =   —————————  •  —————————
(217•520)      (520•216)        (217•520)          1    

Canceling Out :

 6.2      Canceling out  5²⁰ as it appears on both sides of the fraction line

Dividing exponents :

 6.3    2¹⁶   divided by   2¹⁷   = 2^{(16 - 17)} = 2^(-1) = ¹/_2¹ = ¹/₂

Final result :

  1           
  — = 0.50000 
  2