Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-7" was replaced by "^(-7)".

(2): "8.2" was replaced by "(82/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   41 82
  (——•——)•((2)(-7)•(5)(-7))
   10 10

Step  2  :

            41
 Simplify   ——
            5 

Equation at the end of step  2  :

   41   41
  (—— • ——) • ((2)(-7)•(5)(-7))
   10   5 

Step  3  :

 3.1     10 = 2•5

(10)⁶ = (2•5)⁶ = 2⁶ • 5⁶

Equation at the end of step  3  :

   41   41
  (—— • ——) • ((2)(-7)•(5)(-7))
   10   5 

Step  4  :

                      41
 Divide  (26•56)  by  ——
                      5 

Multiplying exponents :

 4.1    5⁶  multiplied by  5¹   = 5^{(6 + 1)} = 5⁷

Equation at the end of step  4  :

   41   (26•57)
  (—— • ———————) • ((2)(-7)•(5)(-7))
   10     41   

Step  5  :

            41
 Simplify   ——
            10

Equation at the end of step  5  :

   41   (26•57)
  (—— • ———————) • ((2)(-7)•(5)(-7))
   10     41   

Step  6  :

Dividing exponents :

 6.1    2⁶   divided by   2¹   = 2^{(6 - 1)} = 2⁵

Dividing exponents :

 6.2    5⁷   divided by   5¹   = 5^{(7 - 1)} = 5⁶

Equation at the end of step  6  :

  (25•56) • ((2)(-7)•(5)(-7))

Step  7  :

Final result :

     1                                      
  ——————— = 10.00000 • 10-8 
  (27•57)