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): "2.4" was replaced by "(24/10)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   24
  (—— • (10-9)) ÷ (6 • ((2)(-6)•(5)(-6)))
   10

Step  2  :

Raising to a Power :

 2.1    2¹   divided by   2⁶   = 2^{(1 - 6)} = 2^(-5) = ¹/_2⁵

Equation at the end of step  2  :

   24                3   
  (—— • (10-9)) ÷ ———————
   10             (25•56)

Step  3  :

 3.1     10 = 2•5

(10)^-9 = (2•5)^(-9) = (2)^(-9) • (5)^(-9)

Equation at the end of step  3  :

   24                           3   
  (—— • ((2)(-9)•(5)(-9))) ÷ ———————
   10                        (25•56)

Step  4  :

            12
 Simplify   ——
            5 

Equation at the end of step  4  :

  12                           3   
  —— • ((2)(-9)•(5)(-9))) ÷ ———————
  5                         (25•56)

Step  5  :

Multiplying exponents :

 5.1    5¹  multiplied by  5⁹   = 5^{(1 + 9)} = 5¹⁰

Dividing exponents :

 5.2    2²   divided by   2⁹   = 2^{(2 - 9)} = 2^(-7) = ¹/_2⁷

Equation at the end of step  5  :

      3         3   
  ———————— ÷ ———————
  (510•27)    (25•56)

Step  6  :

             3            3   
 Divide  ————————  by  ———————
         (510•27)       (25•56)

 6.1    Dividing fractions

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

    3           3              3        (25•56)
————————  ÷  ———————   =   ————————  •  ———————
(510•27)      (25•56)       (510•27)         3   

Dividing exponents :

 6.2    2⁵   divided by   2⁷   = 2^{(5 - 7)} = 2^(-2) = ¹/_2²

Dividing exponents :

 6.3    5⁶   divided by   5¹⁰   = 5^{(6 - 10)} = 5^(-4) = ¹/_5⁴

Final result :

    1            
  ———— = 0.00040 
  2500