Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "0.2" was replaced by "(2/10)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

    2
  (—— • (105)) • (4 • ((2)(-12)•(5)(-12)))
   10

Step  2  :

Raising to a Power :

 2.1    2²   divided by   2¹²   = 2^{(2 - 12)} = 2^(-10) = ¹/_2¹⁰

Equation at the end of step  2  :

    2                1    
  (—— • (105)) • —————————
   10            (210•512) 

Step  3  :

 3.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  3  :

    2                  1    
  (—— • (25•55)) • —————————
   10              (210•512) 

Step  4  :

            1
 Simplify   —
            5

Equation at the end of step  4  :

   1                  1    
  (— • (25•55)) • —————————
   5              (210•512) 

Step  5  :

Dividing exponents :

 5.1    5⁵   divided by   5¹   = 5^{(5 - 1)} = 5⁴

Equation at the end of step  5  :

                1    
  (25•54) • —————————
            (210•512) 

Step  6  :

Dividing exponents :

 6.1    2⁵   divided by   2¹⁰   = 2^{(5 - 10)} = 2^(-5) = ¹/_2⁵

Dividing exponents :

 6.2    5⁴   divided by   5¹²   = 5^{(4 - 12)} = 5^(-8) = ¹/_5⁸

Final result :

     1                                     
  ——————— = 8.00000 • 10-8 
  (25•58)