Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.055" was replaced by "(055/1000)". 2 more similar replacement(s)

Step  1  :

             11
 Simplify   ———
            200

Equation at the end of step  1  :

   30      11
  (——•((1+——— ÷ 2)2))•5
   1      200

Step  2  :

          11      
 Divide  ———  by  2
         200      

Equation at the end of step  2  :

   30           11
  (—— • ((1 +  ———)2)) • 5
   1           400

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  400  as the denominator :

          1     1 • 400
     1 =  —  =  ———————
          1       400  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 3.2       Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 400 + 11     411
 ————————  =  ———
   400        400

Equation at the end of step  3  :

   30    411
  (—— • (———)2)) • 5
   1     400

Step  4  :

 4.1     411 = 3•137

(411)² = (3•137)² = 3² • 137²  4.2     400 = 2⁴•5² (400)² = (2⁴•5²)² = 2⁸ • 5⁴

Equation at the end of step  4  :

   30   (32•1372)
  (—— • —————————) • 5
   1     (28•54) 

Step  5  :

            30
 Simplify   ——
            1 

Equation at the end of step  5  :

        (32•1372)
  (30 • —————————) • 5
         (28•54) 

Step  6  :

Multiplying exponents :

 6.1    3¹  multiplied by  3²   = 3^{(1 + 2)} = 3³

Dividing exponents :

 6.2    2¹   divided by   2⁸   = 2^{(1 - 8)} = 2^(-7) = ¹/_2⁷

Dividing exponents :

 6.3    5¹   divided by   5⁴   = 5^{(1 - 4)} = 5^(-3) = ¹/_5³

Equation at the end of step  6  :

  (33•1372)
  ————————— • 5
   (27•53) 

Step  7  :

Dividing exponents :

 7.1    5¹   divided by   5³   = 5^{(1 - 3)} = 5^(-2) = ¹/_5²

Final result :

  (33•1372)             
  ————————— = 158.36344 
    3200