Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-6" was replaced by "^(-6)". 1 more similar replacement(s)

(2): "9.24" was replaced by "(924/100)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

  )924
  ———— • ((2)(-6)•(5)(-6)))
  (100

Step  2  :

            231
 Simplify   ———
            25 

Equation at the end of step  2  :

  231
  ——— • ((2)(-6)•(5)(-6)))
  (25

Step  3  :

Raising to a Power :

 3.1    5²  multiplied by  5⁶   = 5^{(2 + 6)} = 5⁸

Equation at the end of step  3  :

  ))231 
  ———————
  (58•26)

Step  4  :

 4.1     10 = 2•5

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

Equation at the end of step  4  :

  ))231 
  ———————
  (58•26)

Step  5  :

Equation at the end of step  5  :

     9        231  
  ——————— ÷ ———————
  (25•55)   (58•26)

Step  6  :

            9           231  
 Divide  ———————  by  ———————
         (25•55)      (58•26)

 6.1    Dividing fractions

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

   9          231            9        (58•26)
———————  ÷  ———————   =   ———————  •  ———————
(25•55)     (58•26)       (25•55)       231  

Dividing exponents :

 6.2    3²   divided by   3¹   = 3^{(2 - 1)} = 3¹ = 3

Dividing exponents :

 6.3    5⁸   divided by   5⁵   = 5^{(8 - 5)} = 5³

Dividing exponents :

 6.4    2⁶   divided by   2⁵   = 2^{(6 - 5)} = 2¹ = 2

Final result :

  750           
  ——— = 9.74026 
  77