Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.19" was replaced by "(419/100)". 2 more similar replacement(s)

Step  1  :

            419
 Simplify   ———
            100

Equation at the end of step  1  :

   892             419
  (——— • (104)) +  ———
   100             100

Step  2  :

 2.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  2  :

   892               419
  (——— • (24•54)) +  ———
   100               100

Step  3  :

            223
 Simplify   ———
            25 

Equation at the end of step  3  :

   223               419
  (——— • (24•54)) +  ———
   25                100

Step  4  :

Dividing exponents :

 4.1    5⁴   divided by   5²   = 5^{(4 - 2)} = 5²

Equation at the end of step  4  :

                 419
  (223•24•52) +  ———
                 100

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  100  as the denominator :

                    (223•24•52)     (223•24•52) • 100
     (223•24•52) =  ———————————  =  —————————————————
                         1                 100       

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 :

 5.2       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:

Multiplying exponents :

 2⁴  multiplied by  2²   = 2^{(4 + 2)} = 2⁶

Multiplying exponents :

 5²  multiplied by  5²   = 5^{(2 + 2)} = 5⁴ (223•2⁴•5²) • 100 + 419 223•2⁶•5⁴ + 419 ——————————————————————— = ——————————————— 100 100

Final result :

  223 + 419
  —————————
     100