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): "2.5" was replaced by "(25/10)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   25
  (—— • (10-10)) • (7 • ((2)(-6)•(5)(-6)))
   10

Step  2  :

Equation at the end of step  2  :

   25                 7   
  (—— • (10-10)) • ———————
   10              (26•56)

Step  3  :

 3.1     10 = 2•5

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

Equation at the end of step  3  :

   25                             7   
  (—— • ((2)(-10)•(5)(-10))) • ———————
   10                          (26•56)

Step  4  :

            5
 Simplify   —
            2

Equation at the end of step  4  :

   5                             7   
  (— • ((2)(-10)•(5)(-10))) • ———————
   2                          (26•56)

Step  5  :

Multiplying exponents :

 5.1    2¹  multiplied by  2¹⁰   = 2^{(1 + 10)} = 2¹¹

Dividing exponents :

 5.2    5¹   divided by   5¹⁰   = 5^{(1 - 10)} = 5^(-9) = ¹/_5⁹

Equation at the end of step  5  :

      1         7   
  ———————— • ———————
  (211•59)    (26•56)

Step  6  :

Multiplying exponents :

 6.1    2¹¹  multiplied by  2⁶   = 2^{(11 + 6)} = 2¹⁷

Multiplying exponents :

 6.2    5⁹  multiplied by  5⁶   = 5^{(9 + 6)} = 5¹⁵

Final result :

      7                                       
  ————————— = 1.75000 • 10-15 
  (217•515)