Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-12" was replaced by "^(-12)".

Step  1  :

 1.1     10 = 2•5

(10)^-12 = (2•5)^(-12) = (2)^(-12) • (5)^(-12)

Equation at the end of step  1  :

  ((2 • (107)) • 8) • ((2)(-12)•(5)(-12))

Step  2  :

 2.1     10 = 2•5

(10)⁷ = (2•5)⁷ = 2⁷ • 5⁷

Equation at the end of step  2  :

  ((2 • (27•57)) • 8) • ((2)(-12)•(5)(-12))

Step  3  :

Multiplying exponents :

 3.1    2¹  multiplied by  2⁷   = 2^{(1 + 7)} = 2⁸

Equation at the end of step  3  :

  ((28•57) • 8) • ((2)(-12)•(5)(-12))

Step  4  :

Multiplying exponents :

 4.1    2⁸  multiplied by  2³   = 2^{(8 + 3)} = 2¹¹

Equation at the end of step  4  :

  (211•57) • ((2)(-12)•(5)(-12))

Step  5  :

Dividing exponents :

 5.1    2¹¹   divided by   2¹²   = 2^{(11 - 12)} = 2^(-1) = ¹/_2¹ = ¹/₂

Dividing exponents :

 5.2    5⁷   divided by   5¹²   = 5^{(7 - 12)} = 5^(-5) = ¹/_5⁵

Final result :

    1            
  ———— = 0.00016 
  6250