Solution - Power equations

Step  1  :

 1.1     35 = 5•7

(35)² = (5•7)² = 5² • 7²

Equation at the end of step  1  :

              (52•72)
  100 • (1 -  ——————— ÷ 1000)
                250  

Step  2  :

            (52•72)
 Simplify   ———————
              250  

Dividing exponents :

 2.1    5²   divided by   5³   = 5^{(2 - 3)} = 5^(-1) = ¹/_5¹ = ¹/₅

Equation at the end of step  2  :

              49
  100 • (1 -  —— ÷ 1000)
              10

Step  3  :

         49      
 Divide  ——  by  1000
         10      

Equation at the end of step  3  :

                49 
  100 • (1 -  —————)
              10000

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  10000  as the denominator :

          1     1 • 10000
     1 =  —  =  —————————
          1       10000  

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 :

 4.2       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:

 10000 - (49)      9951
 ————————————  =  —————
    10000         10000

Equation at the end of step  4  :

         9951
  100 • —————
        10000

Step  5  :

Final result :

  9951            
  ———— = 99.51000 
  100