Solution - Power equations

Step  1  :

            1
 Simplify   —
            6

Equation at the end of step  1  :

  (1443)    1
  —————— -  —
    2       6

Step  2  :

 2.1     144 = 24•32

(144)³ = (2⁴•3²)³ = 2¹² • 3⁶

Equation at the end of step  2  :

  (212•36)     1
  ———————— -  —
     2        6

Step  3  :

            (212•36) 
 Simplify   ————————
               2    

Dividing exponents :

 3.1    2¹²   divided by   2¹   = 2^{(12 - 1)} = 2¹¹

Equation at the end of step  3  :

              1
  (211•36) -  —
              6

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  6  as the denominator :

                 (211•36)      (211•36) • 6 
     (211•36) =  ————————  =  ————————————
                    1              6      

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:

Multiplying exponents :

 2¹¹  multiplied by  2¹   = 2^{(11 + 1)} = 2¹²

Multiplying exponents :

 3⁶  multiplied by  3¹   = 3^{(6 + 1)} = 3⁷ (2¹¹•3⁶) • 6 - (1) 2¹²•3⁷ - 1 —————————————————— = —————————— 6 6

Final result :

  144 - 1
  ———————
     6