Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "37.9" was replaced by "(379/10)". 2 more similar replacement(s)

Step  1  :

            379
 Simplify   ———
            10 

Equation at the end of step  1  :

   912             379
  (——— • (105)) -  ———
   100             10 

Step  2  :

 2.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  2  :

   912               379
  (——— • (25•55)) -  ———
   100               10 

Step  3  :

            228
 Simplify   ———
            25 

Equation at the end of step  3  :

   228               379
  (——— • (25•55)) -  ———
   25                10 

Step  4  :

Multiplying exponents :

 4.1    2²  multiplied by  2⁵   = 2^{(2 + 5)} = 2⁷

Dividing exponents :

 4.2    5⁵   divided by   5²   = 5^{(5 - 2)} = 5³

Equation at the end of step  4  :

                  379
  (27•3•19•53) -  ———
                  10 

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  10  as the denominator :

                     (27•3•19•53)     (27•3•19•53) • 10
     (27•3•19•53) =  ————————————  =  —————————————————
                          1                  10        

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 :

 2⁷  multiplied by  2¹   = 2^{(7 + 1)} = 2⁸

Multiplying exponents :

 5³  multiplied by  5¹   = 5^{(3 + 1)} = 5⁴ (2⁷•3•19•5³) • 10 - (379) 2⁸•3•19•5⁴ - 379 ————————————————————————— = ———————————————— 10 10

Final result :

  228 - 379
  —————————
     10