Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "0.38" was replaced by "(38/100)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  1  :

   51           38
  (——•(10-1))+(———•(24•54))
   10          100

Step  2  :

            19
 Simplify   ——
            50

Equation at the end of step  2  :

   51               19
  (—— • (10-1)) +  (—— • (24•54))
   10               50

Step  3  :

Dividing exponents :

 3.1    2⁴   divided by   2¹   = 2^{(4 - 1)} = 2³

Raising to a Power :

 3.2    5⁴   divided by   5²   = 5^{(4 - 2)} = 5²

Equation at the end of step  3  :

   51               
  (—— • (10-1)) +  3800
   10               

Step  4  :

 4.1     10 = 2•5

(10)^-1 = (2•5)^(-1) = (2)^(-1) • (5)^(-1)

Equation at the end of step  4  :

   51                           
  (—— • ((2)(-1)•(5)(-1))) +  3800
   10                           

Step  5  :

            51
 Simplify   ——
            10

Equation at the end of step  5  :

   51                           
  (—— • ((2)(-1)•(5)(-1))) +  3800
   10                           

Step  6  :

Multiplying exponents :

 6.1    2¹  multiplied by  2¹   = 2^{(1 + 1)} = 2²

Multiplying exponents :

 6.2    5¹  multiplied by  5¹   = 5^{(1 + 1)} = 5²

Equation at the end of step  6  :

   51    
  ——— +  3800
  100    

Step  7  :

Rewriting the whole as an Equivalent Fraction :

 7.1   Adding a whole to a fraction

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

            3800     3800 • 100
    3800 =  ————  =  ——————————
             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 :

 7.2       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:

 51 + 3800 • 100     380051
 ———————————————  =  ——————
       100            100  

Final result :

  380051              
  —————— = 3800.51000 
   100