Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-10" was replaced by "^(-10)". 1 more similar replacement(s)

(2): "5.5" was replaced by "(55/10)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   55
  (—— • (10-8)) ÷ (3 • ((2)(-10)•(5)(-10)))
   10

Step  2  :

Equation at the end of step  2  :

   55                 3    
  (—— • (10-8)) ÷ —————————
   10             (210•510) 

Step  3  :

 3.1     10 = 2•5

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

Equation at the end of step  3  :

   55                            3    
  (—— • ((2)(-8)•(5)(-8))) ÷ —————————
   10                        (210•510) 

Step  4  :

            11
 Simplify   ——
            2 

Equation at the end of step  4  :

  11                            3    
  —— • ((2)(-8)•(5)(-8))) ÷ —————————
  2                         (210•510) 

Step  5  :

Multiplying exponents :

 5.1    2¹  multiplied by  2⁸   = 2^{(1 + 8)} = 2⁹

Equation at the end of step  5  :

     11         3    
  ——————— ÷ —————————
  (29•58)   (210•510) 

Step  6  :

            11            3    
 Divide  ———————  by  —————————
         (29•58)      (210•510) 

 6.1    Dividing fractions

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

   11           3              11       (210•510) 
———————  ÷  —————————   =   ———————  •  —————————
(29•58)     (210•510)        (29•58)         3    

Dividing exponents :

 6.2    2¹⁰   divided by   2⁹   = 2^{(10 - 9)} = 2¹ = 2

Dividing exponents :

 6.3    5¹⁰   divided by   5⁸   = 5^{(10 - 8)} = 5²

Final result :

  550             
  ——— = 183.33333 
   3