Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

  (7 • (108)) • ((3 • ((2)(-7)•(5)(-7)))2)

Step  2  :

Equation at the end of step  2  :

                    3   
  (7 • (108)) • (———————)2)
                 (27•57)

Step  3  :

Equation at the end of step  3  :

                    32   
  (7 • (108)) • —————————
                (214•514) 

Step  4  :

 4.1     10 = 2•5

(10)⁸ = (2•5)⁸ = 2⁸ • 5⁸

Equation at the end of step  4  :

                      32   
  (7 • (28•58)) • —————————
                  (214•514) 

Step  5  :

Equation at the end of step  5  :

                  32   
  (7•28•58) • —————————
              (214•514) 

Step  6  :

Dividing exponents :

 6.1    2⁸   divided by   2¹⁴   = 2^{(8 - 14)} = 2^(-6) = ¹/_2⁶

Dividing exponents :

 6.2    5⁸   divided by   5¹⁴   = 5^{(8 - 14)} = 5^(-6) = ¹/_5⁶

Final result :

     63             
  ——————— = 0.00006 
  (26•56)