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  :

 1.1     729 = 36

(729)^-1 = (3⁶)^(-1) = (3)^(-6)

Equation at the end of step  1  :

        (813)
  (3-2)•————— ÷ (3)(-6) ÷ 3
          4  

Step  2  :

 2.1     81 = 34

(81)³ = (3⁴)³ = 3¹²

Equation at the end of step  2  :

          312
  (3-2) • ——— ÷ (3)(-6) ÷ 3
           4 

Step  3  :

            312
 Simplify   ———
             4 

Equation at the end of step  3  :

          312
  (3-2) • ——— ÷ (3)(-6) ÷ 3
           4 

Step  4  :

         312      
 Divide  ———  by  (3)(-6)
          4       

 4.1    Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

312      1       312     36
———  ÷  ——   =   ———  •  ——
 4      36        4      1 

Multiplying exponents :

 4.2    3¹²  multiplied by  3⁶   = 3^{(12 + 6)} = 3¹⁸

Equation at the end of step  4  :

          318
  (3-2) • ——— ÷ 3
           4 

Step  5  :

         318      
 Divide  ———  by  3
          4       

Dividing exponents :

 5.1    3¹⁸   divided by   3¹   = 3^{(18 - 1)} = 3¹⁷

Equation at the end of step  5  :

          317
  (3-2) • ———
           4 

Step  6  :

Equation at the end of step  6  :

            317
  (3)(-2) • ———
             4 

Step  7  :

Dividing exponents :

 7.1    3¹⁷   divided by   3²   = 3^{(17 - 2)} = 3¹⁵

Final result :

  315                                 
  ——— = 3.58723 • 106 
   4