Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-6" was replaced by "^(-6))". 1 more similar replacement(s)

(2): ".3" was replaced by "(3/10)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

                    3
  ((5 • (10-33)) • ——) • ((2)(-6)•(5)(-6))
                   10

Step  2  :

             3
 Simplify   ——
            10

Equation at the end of step  2  :

                    3
  ((5 • (10-33)) • ——) • ((2)(-6)•(5)(-6))
                   10

Step  3  :

 3.1     10 = 2•5

(10)^-33 = (2•5)^(-33) = (2)^(-33) • (5)^(-33)

Equation at the end of step  3  :

                                3
  ((5 • ((2)(-33)•(5)(-33))) • ——) • ((2)(-6)•(5)(-6))
                               10

Step  4  :

Dividing exponents :

 4.1    5¹   divided by   5³³   = 5^{(1 - 33)} = 5^(-32) = ¹/_5³²

Equation at the end of step  4  :

       1        3
  (————————— • ——) • ((2)(-6)•(5)(-6))
   (233•532)    10

Step  5  :

Multiplying exponents :

 5.1    2³³  multiplied by  2¹   = 2^{(33 + 1)} = 2³⁴

Multiplying exponents :

 5.2    5³²  multiplied by  5¹   = 5^{(32 + 1)} = 5³³

Equation at the end of step  5  :

      3    
  ————————— • ((2)(-6)•(5)(-6))
  (234•533) 

Step  6  :

Multiplying exponents :

 6.1    2³⁴  multiplied by  2⁶   = 2^{(34 + 6)} = 2⁴⁰

Multiplying exponents :

 6.2    5³³  multiplied by  5⁶   = 5^{(33 + 6)} = 5³⁹

Final result :

      3                                       
  ————————— = 1.50000 • 10-39 
  (240•539)