Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-1" was replaced by "^(-1)". 1 more similar replacement(s)

Step  1  :

Equation at the end of step  1  :

   (((2•(a-3))•(b4))2) 
  (———————————————————-2)-1
         (3a5•b)      
 Step  2  :

Equation at the end of step  2  :

   ((2a(-3) • (b4))2)     
  (—————————————————— -  2)-1
          3a5b           
 Step  3  :
            22a(-6)b8 
 Simplify   —————————
              3a5b   

Dividing exponential expressions :

 3.1    a^(-6) divided by a⁵ = a^{((-6) - 5)} = a^(-11) = ¹/_a¹¹

Dividing exponential expressions :

 3.2    b⁸ divided by b¹ = b^{(8 - 1)} = b⁷

Equation at the end of step  3  :

    4b7    
  (———— -  2)-1
   3a11    

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  3a¹¹  as the denominator :

         2     2 • 3a11
    2 =  —  =  ————————
         1       3a11  

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:

 4b7 - (2 • 3a11)     4b7 - 6a11
 ————————————————  =  ——————————
       3a11              3a11   

Equation at the end of step  4  :

  (4b7 - 6a11)
 (————————————)-1
     (3a11)   

Step  5  :

 5.1    a¹¹ raised to the minus 1 st power = a^{( 11 * -1 )} = a^-11

Step  6  :

Pulling out like terms :

 6.1    Simplify ( 4b⁷-6a¹¹ )^-1

Put the exponent aside and simplfy the base by pulling out like factors :
 4b⁷-6a¹¹  =  -2 • (3a¹¹-2b⁷) 

Remember the 4th law of exponents : (a • b)^m= a^m• b^m

Retract the exponent and apply the 4th law to the simplified base: ( -2 • (3a¹¹-2b⁷) )^-1 =  (-2)^-1 • (3a¹¹-2b⁷)^-1  

Final result :

               3            
  ——————————————————————————
  a(-11) • -2 • (3a11 - 2b7)