Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-11" was replaced by "^(-11)".

(2): "6.67" was replaced by "(667/100)".

Step  1  :

 1.1     10 = 2•5

(10)²⁴ = (2•5)²⁴ = 2²⁴ • 5²⁴

Equation at the end of step  1  :

    667
  ((——— • (10-11)) • 6) • (224•524)
    100

Step  2  :

 2.1     10 = 2•5

(10)^-11 = (2•5)^(-11) = (2)^(-11) • (5)^(-11)

Equation at the end of step  2  :

    667
  ((——— • ((2)(-11)•(5)(-11))) • 6) • (224•524)
    100

Step  3  :

            667
 Simplify   ———
            100

Equation at the end of step  3  :

    667
  ((——— • ((2)(-11)•(5)(-11))) • 6) • (224•524)
    100

Step  4  :

Multiplying exponents :

 4.1    2²  multiplied by  2¹¹   = 2^{(2 + 11)} = 2¹³

Multiplying exponents :

 4.2    5²  multiplied by  5¹¹   = 5^{(2 + 11)} = 5¹³

Equation at the end of step  4  :

      667   
  (————————— • 6) • (224•524)
   (213•513) 

Step  5  :

Dividing exponents :

 5.1    2¹   divided by   2¹³   = 2^{(1 - 13)} = 2^(-12) = ¹/_2¹²

Equation at the end of step  5  :

     2001  
  ————————— • (224•524)
  (212•513) 

Step  6  :

Dividing exponents :

 6.1    2²⁴   divided by   2¹²   = 2^{(24 - 12)} = 2¹²

Dividing exponents :

 6.2    5²⁴   divided by   5¹³   = 5^{(24 - 13)} = 5¹¹

Final result :

  (3•23•29•212•511)