Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-8" was replaced by "^(-8)".

(2): "7.1" was replaced by "(71/10)".

Step  1  :

 1.1     10 = 2•5

(10)^-8 = (2•5)^(-8) = (2)^(-8) • (5)^(-8)

Equation at the end of step  1  :

   71
  (—— • (105)) • (2 • ((2)(-8)•(5)(-8)))
   10

Step  2  :

Raising to a Power :

 2.1    2¹   divided by   2⁸   = 2^{(1 - 8)} = 2^(-7) = ¹/_2⁷

Equation at the end of step  2  :

   71               1   
  (—— • (105)) • ———————
   10            (27•58)

Step  3  :

 3.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  3  :

   71                 1   
  (—— • (25•55)) • ———————
   10              (27•58)

Step  4  :

            71
 Simplify   ——
            10

Equation at the end of step  4  :

   71                 1   
  (—— • (25•55)) • ———————
   10              (27•58)

Step  5  :

Dividing exponents :

 5.1    2⁵   divided by   2¹   = 2^{(5 - 1)} = 2⁴

Dividing exponents :

 5.2    5⁵   divided by   5¹   = 5^{(5 - 1)} = 5⁴

Equation at the end of step  5  :

                  1   
  (71•24•54) • ———————
               (27•58)

Step  6  :

Dividing exponents :

 6.1    2⁴   divided by   2⁷   = 2^{(4 - 7)} = 2^(-3) = ¹/_2³

Dividing exponents :

 6.2    5⁴   divided by   5⁸   = 5^{(4 - 8)} = 5^(-4) = ¹/_5⁴

Final result :

   71            
  ———— = 0.01420 
  5000