Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-5" was replaced by "^(-5))". 1 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

Step  2  :

Raising to a Power :

 2.1    2¹   divided by   2⁵   = 2^{(1 - 5)} = 2^(-4) = ¹/_2⁴

Equation at the end of step  2  :

  2))1 
  ———————
  (24•55)

Step  3  :

 3.1     10 = 2•5

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

Equation at the end of step  3  :

  )))1 
  ———————
  (24•55)

Step  4  :

Equation at the end of step  4  :

      3          1   
  ————————— ÷ ———————
  (212•512)    (24•55)

Step  5  :

             3             1   
 Divide  —————————  by  ———————
         (212•512)       (24•55)

 5.1    Dividing fractions

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

    3            1              3         (24•55)
—————————  ÷  ———————   =   —————————  •  ———————
(212•512)      (24•55)       (212•512)         1   

Dividing exponents :

 5.2    2⁴   divided by   2¹²   = 2^{(4 - 12)} = 2^(-8) = ¹/_2⁸

Dividing exponents :

 5.3    5⁵   divided by   5¹²   = 5^{(5 - 12)} = 5^(-7) = ¹/_5⁷

Final result :

     3                                     
  ——————— = 1.50000 • 10-7 
  (28•57)