Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-6" was replaced by "^(-6)".

(2): "1.2" was replaced by "(12/10)".

Step  1  :

 1.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  1  :

   12   (10-6)
  (—— • ——————) • (23•53)
   10     4   

Step  2  :

 2.1     10 = 2•5

(10)^-6 = (2•5)^(-6) = (2)^(-6) • (5)^(-6)

Equation at the end of step  2  :

   12   ((2)(-6)•(5)(-6)) 
  (—— • —————————————————) • (23•53)
   10           4        

Step  3  :

            1         
 Divide  ———————  by  4
         (26•56)      

Multiplying exponents :

 3.1    2⁶  multiplied by  2²   = 2^{(6 + 2)} = 2⁸

Equation at the end of step  3  :

   12      1   
  (—— • ———————) • (23•53)
   10   (28•56)

Step  4  :

            6
 Simplify   —
            5

Equation at the end of step  4  :

   6      1   
  (— • ———————) • (23•53)
   5   (28•56)

Step  5  :

Multiplying exponents :

 5.1    5¹  multiplied by  5⁶   = 5^{(1 + 6)} = 5⁷

Dividing exponents :

 5.2    2¹   divided by   2⁸   = 2^{(1 - 8)} = 2^(-7) = ¹/_2⁷

Equation at the end of step  5  :

     3   
  ——————— • (23•53)
  (57•27)

Step  6  :

Dividing exponents :

 6.1    2³   divided by   2⁷   = 2^{(3 - 7)} = 2^(-4) = ¹/_2⁴

Dividing exponents :

 6.2    5³   divided by   5⁷   = 5^{(3 - 7)} = 5^(-4) = ¹/_5⁴

Final result :

     3              
  ——————— = 0.00030 
  (54•24)