Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "1.58" was replaced by "(158/100)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   4 314   158
  (—•———)•(———•((2)(-8)•(5)(-8)))
   3 100   100

Step  2  :

            79
 Simplify   ——
            50

Equation at the end of step  2  :

   4   314     79
  (— • ———) • (—— • ((2)(-8)•(5)(-8)))
   3   100     50

Step  3  :

Multiplying exponents :

 3.1    2¹  multiplied by  2⁸   = 2^{(1 + 8)} = 2⁹

Multiplying exponents :

 3.2    5²  multiplied by  5⁸   = 5^{(2 + 8)} = 5¹⁰

Equation at the end of step  3  :

   4   314       79   
  (— • ———) • ————————
   3   100    (29•510) 

Step  4  :

            157
 Simplify   ———
            50 

Equation at the end of step  4  :

   4   157       79   
  (— • ———) • ————————
   3   50     (29•510) 

Step  5  :

            4
 Simplify   —
            3

Equation at the end of step  5  :

   4   157       79   
  (— • ———) • ————————
   3   50     (29•510) 

Step  6  :

Multiplying exponents :

 6.1    5²  multiplied by  5¹⁰   = 5^{(2 + 10)} = 5¹²

Dividing exponents :

 6.2    2¹   divided by   2⁹   = 2^{(1 - 9)} = 2^(-8) = ¹/_2⁸

Final result :

   (79•157)                                   
  —————————— = 6.61493 • 10-8 
  (3•512•28)