Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-7" was replaced by "^(-7))". 1 more similar replacement(s)

(2): "1.8" was replaced by "(18/10)".

Step  1  :

 1.1     10 = 2•5

(10)^-7 = (2•5)^(-7) = (2)^(-7) • (5)^(-7)

Equation at the end of step  1  :

   18
  (—— • (10-10)) ÷ (6 • ((2)(-7)•(5)(-7)))
   10

Step  2  :

Raising to a Power :

 2.1    2¹   divided by   2⁷   = 2^{(1 - 7)} = 2^(-6) = ¹/_2⁶

Equation at the end of step  2  :

   18                 3   
  (—— • (10-10)) ÷ ———————
   10              (26•57)

Step  3  :

 3.1     10 = 2•5

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

Equation at the end of step  3  :

   18                             3   
  (—— • ((2)(-10)•(5)(-10))) ÷ ———————
   10                          (26•57)

Step  4  :

            9
 Simplify   —
            5

Equation at the end of step  4  :

  9                             3   
  — • ((2)(-10)•(5)(-10))) ÷ ———————
  5                          (26•57)

Step  5  :

Multiplying exponents :

 5.1    5¹  multiplied by  5¹⁰   = 5^{(1 + 10)} = 5¹¹

Equation at the end of step  5  :

      9          3   
  ————————— ÷ ———————
  (511•210)    (26•57)

Step  6  :

             9             3   
 Divide  —————————  by  ———————
         (511•210)       (26•57)

 6.1    Dividing fractions

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

    9            3              9         (26•57)
—————————  ÷  ———————   =   —————————  •  ———————
(511•210)      (26•57)       (511•210)         3   

Dividing exponents :

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

Dividing exponents :

 6.3    2⁶   divided by   2¹⁰   = 2^{(6 - 10)} = 2^(-4) = ¹/_2⁴

Dividing exponents :

 6.4    5⁷   divided by   5¹¹   = 5^{(7 - 11)} = 5^(-4) = ¹/_5⁴

Final result :

     3              
  ——————— = 0.00030 
  (54•24)