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): "1.3" was replaced by "(13/10)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   13
  (—— • (10-6)) • (2 • ((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  :

   13                1   
  (—— • (10-6)) • ———————
   10             (26•57)

Step  3  :

 3.1     10 = 2•5

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

Equation at the end of step  3  :

   13                           1   
  (—— • ((2)(-6)•(5)(-6))) • ———————
   10                        (26•57)

Step  4  :

            13
 Simplify   ——
            10

Equation at the end of step  4  :

   13                           1   
  (—— • ((2)(-6)•(5)(-6))) • ———————
   10                        (26•57)

Step  5  :

Multiplying exponents :

 5.1    2¹  multiplied by  2⁶   = 2^{(1 + 6)} = 2⁷

Multiplying exponents :

 5.2    5¹  multiplied by  5⁶   = 5^{(1 + 6)} = 5⁷

Equation at the end of step  5  :

     13        1   
  ——————— • ———————
  (27•57)   (26•57)

Step  6  :

Multiplying exponents :

 6.1    2⁷  multiplied by  2⁶   = 2^{(7 + 6)} = 2¹³

Multiplying exponents :

 6.2    5⁷  multiplied by  5⁷   = 5^{(7 + 7)} = 5¹⁴

Final result :

      13                                      
  ————————— = 2.60000 • 10-13 
  (213•514)