Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.02" was replaced by "(102/100)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)¹ = (2•5)¹ = 2 • 5

Equation at the end of step  1  :

   205         102
  (———•(102))+(———•(2•5))
   100         100

Step  2  :

            51
 Simplify   ——
            50

Equation at the end of step  2  :

   205              51
  (——— • (102)) +  (—— • (2•5))
   100              50

Step  3  :

Canceling Out :

 3.1      Canceling out  2  as it appears on both sides of the fraction line

Raising to a Power :

 3.2    5¹   divided by   5²   = 5^{(1 - 2)} = 5^(-1) = ¹/_5¹ = ¹/₅

Equation at the end of step  3  :

   205             51
  (——— • (102)) +  ——
   100             5 

Step  4  :

 4.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  4  :

   205               51
  (——— • (22•52)) +  ——
   100               5 

Step  5  :

            41
 Simplify   ——
            20

Equation at the end of step  5  :

   41               51
  (—— • (22•52)) +  ——
   20               5 

Step  6  :

Canceling Out :

 6.1      Canceling out  2² as it appears on both sides of the fraction line

Dividing exponents :

 6.2    5²   divided by   5¹   = 5^{(2 - 1)} = 5¹ = 5

Equation at the end of step  6  :

         51
  205 +  ——
         5 

Step  7  :

Rewriting the whole as an Equivalent Fraction :

 7.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  5  as the denominator :

            205     205 • 5
     205 =  ———  =  ———————
             1         5   

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:

 205 • 5 + 51     1076
 ————————————  =  ————
      5            5  

Final result :

  1076             
  ———— = 215.20000 
   5