Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.047" was replaced by "(4047/1000)". 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  :

   32         4047
  (——•(102))+(————•(22•52))
   10         1000

Step  2  :

            4047
 Simplify   ————
            1000

Equation at the end of step  2  :

   32              4047
  (—— • (102)) +  (———— • (22•52))
   10              1000

Step  3  :

Dividing exponents :

 3.1    2²   divided by   2³   = 2^{(2 - 3)} = 2^(-1) = ¹/_2¹ = ¹/₂

Raising to a Power :

 3.2    5²   divided by   5³   = 5^{(2 - 3)} = 5^(-1) = ¹/_5¹ = ¹/₅

Equation at the end of step  3  :

   32             4047
  (—— • (102)) +  ————
   10              10 

Step  4  :

 4.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  4  :

   32               4047
  (—— • (22•52)) +  ————
   10                10 

Step  5  :

            16
 Simplify   ——
            5 

Equation at the end of step  5  :

   16               4047
  (—— • (22•52)) +  ————
   5                 10 

Step  6  :

Multiplying exponents :

 6.1    2⁴  multiplied by  2²   = 2^{(4 + 2)} = 2⁶

Dividing exponents :

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

Equation at the end of step  6  :

         4047
  320 +  ————
          10 

Step  7  :

Rewriting the whole as an Equivalent Fraction :

 7.1   Adding a fraction to a whole

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

            320     320 • 10
     320 =  ———  =  ————————
             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 :

 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:

 320 • 10 + 4047     7247
 ———————————————  =  ————
       10             10 

Final result :

  7247             
  ———— = 724.70000 
   10