Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.12" was replaced by "(12/100)".

Step  1  :

             3
 Simplify   ——
            25

Equation at the end of step  1  :

                   3
  422000 • ((1 +  ——)8)
                  25

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  25  as the denominator :

          1     1 • 25
     1 =  —  =  ——————
          1       25  

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 :

 2.2       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:

 25 + 3     28
 ——————  =  ——
   25       25

Equation at the end of step  2  :

            28
  422000 • (——)8)
            25

Step  3  :

 3.1     28 = 22•7

(28)⁸ = (2²•7)⁸ = 2¹⁶ • 7⁸  3.2     25 = 5² (25)⁸ = (5²)⁸ = 5¹⁶

Equation at the end of step  3  :

           (216•78)
  422000 • ————————
             516   

Step  4  :

Multiplying exponents :

 4.1    2⁴  multiplied by  2¹⁶   = 2^{(4 + 16)} = 2²⁰

Dividing exponents :

 4.2    5³   divided by   5¹⁶   = 5^{(3 - 16)} = 5^(-13) = ¹/_5¹³

Final result :

  (220•211•78)                                 
  ———————————— = 1.04486 • 106 
      513