Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-15" was replaced by "^(-15)".

(2): "4.136" was replaced by "(4136/1000)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)^-15 = (2•5)^(-15) = (2)^(-15) • (5)^(-15)

Equation at the end of step  1  :

   306    4136
  ———— ÷ (———— • ((2)(-15)•(5)(-15)))
  1000    1000

Step  2  :

            517
 Simplify   ———
            125

Equation at the end of step  2  :

   306    517
  ———— ÷ (——— • ((2)(-15)•(5)(-15)))
  1000    125

Step  3  :

Multiplying exponents :

 3.1    5³  multiplied by  5¹⁵   = 5^{(3 + 15)} = 5¹⁸

Equation at the end of step  3  :

   306      517   
  ———— ÷ —————————
  1000   (518•215) 

Step  4  :

            153
 Simplify   ———
            500

Equation at the end of step  4  :

  153      517   
  ——— ÷ —————————
  500   (518•215) 

Step  5  :

         153         517   
 Divide  ———  by  —————————
         500      (518•215) 

 5.1    Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

153        517          153     (518•215) 
———  ÷  —————————   =   ———  •  —————————
500     (518•215)        500        517   

Dividing exponents :

 5.2    5¹⁸   divided by   5³   = 5^{(18 - 3)} = 5¹⁵

Dividing exponents :

 5.3    2¹⁵   divided by   2²   = 2^{(15 - 2)} = 2¹³

Final result :

  (32•17•515•213)                                   
  ——————————————— = 7.39845 • 1013 
        517