Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.25" was replaced by "(25/100)". 2 more similar replacement(s)

Step  1  :

            1
 Simplify   —
            4

Equation at the end of step  1  :

     25            1    
  ((——— -  x)3) • (— -  x)
    100            4    

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  4  as the denominator :

         x     x • 4
    x =  —  =  —————
         1       4  

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:

 1 - (x • 4)     1 - 4x
 ———————————  =  ——————
      4            4   

Equation at the end of step  2  :

     25           (1 - 4x)
  ((——— -  x)3) • ————————
    100              4    

Step  3  :

            1
 Simplify   —
            4

Equation at the end of step  3  :

    1           (1 - 4x)
  ((— -  x)3) • ————————
    4              4    

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  4  as the denominator :

         x     x • 4
    x =  —  =  —————
         1       4  

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions

 1 - (x • 4)     1 - 4x
 ———————————  =  ——————
      4            4   

Equation at the end of step  4  :

   (1 - 4x)      (1 - 4x)
  (————————)3) • ————————
      4             4    

Step  5  :

 5.1     4 = 22

(4)³ = (2²)³ = 2⁶

Equation at the end of step  5  :

  (1 - 4x)3   (1 - 4x)
  ————————— • ————————
     26          4    

Step  6  :

Multiplying exponents :

 6.1    2⁶  multiplied by  2²   = 2^{(6 + 2)} = 2⁸

Multiplying Exponential Expressions :

 6.2    Multiply  (1-4x)³   by  (1-4x) 

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (1-4x)  and the exponents are :
          3
 and   1 , as  (1-4x)  is the same number as  (1-4x)¹ 
The product is therefore,  (1-4x)⁽³⁺¹⁾ = (1-4x)⁴ 

Final result :

  (1 - 4x)4
  —————————
     28