Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-16" was replaced by "^(-16)".

Step  1  :

 1.1     10 = 2•5

(10)^-16 = (2•5)^(-16) = (2)^(-16) • (5)^(-16)

Equation at the end of step  1  :

  (9 • (107)) • (3 • ((2)(-16)•(5)(-16)))

Step  2  :

Equation at the end of step  2  :

                    3    
  (9 • (107)) • —————————
                (216•516) 

Step  3  :

 3.1     10 = 2•5

(10)⁷ = (2•5)⁷ = 2⁷ • 5⁷

Equation at the end of step  3  :

                      3    
  (9 • (27•57)) • —————————
                  (216•516) 

Step  4  :

Equation at the end of step  4  :

                   3    
  (32•27•57) • —————————
               (216•516) 

Step  5  :

Multiplying exponents :

 5.1    3²  multiplied by  3¹   = 3^{(2 + 1)} = 3³

Dividing exponents :

 5.2    2⁷   divided by   2¹⁶   = 2^{(7 - 16)} = 2^(-9) = ¹/_2⁹

Dividing exponents :

 5.3    5⁷   divided by   5¹⁶   = 5^{(7 - 16)} = 5^(-9) = ¹/_5⁹

Final result :

     27                                    
  ——————— = 2.70000 • 10-8 
  (29•59)