Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.1" was replaced by "(1/10)".

Step  1  :

             1
 Simplify   ——
            10

Equation at the end of step  1  :

                   1
  100000 • ((1 -  ——)3)
                  10

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole

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

          1     1 • 10
     1 =  —  =  ——————
          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 :

 2.2       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:

 10 - (1)      9
 ————————  =  ——
    10        10

Equation at the end of step  2  :

             9
  100000 • (——)3)
            10

Step  3  :

 3.1     9 = 32

(9)³ = (3²)³ = 3⁶  3.2     10 = 2•5 (10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  3  :

              36  
  100000 • ———————
           (23•53)

Step  4  :

Dividing exponents :

 4.1    2⁵   divided by   2³   = 2^{(5 - 3)} = 2²

Dividing exponents :

 4.2    5⁵   divided by   5³   = 5^{(5 - 3)} = 5²

Final result :

  (22•52•36)