Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.5" was replaced by "(45/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  1  :

  1034     45
  ———— -  (—— • (22•52))
  1000     10

Step  2  :

            9
 Simplify   —
            2

Equation at the end of step  2  :

  1034     9
  ———— -  (— • (22•52))
  1000     2

Step  3  :

Dividing exponents :

 3.1    2²   divided by   2¹   = 2^{(2 - 1)} = 2¹ = 2

Equation at the end of step  3  :

  1034    
  ———— -  450
  1000    

Step  4  :

            517
 Simplify   ———
            500

Equation at the end of step  4  :

  517    
  ——— -  450
  500    

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  500  as the denominator :

           450     450 • 500
    450 =  ———  =  —————————
            1         500   

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:

 517 - (450 • 500)     -224483
 —————————————————  =  ———————
        500              500  

Final result :

  -224483              
  ——————— = -448.96600 
    500