Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "4.54" was replaced by "(454/100)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   454
  (——— • (108)) ÷ (3 • ((2)(-6)•(5)(-6)))
   100

Step  2  :

Equation at the end of step  2  :

   454               3   
  (——— • (108)) ÷ ———————
   100            (26•56)

Step  3  :

 3.1     10 = 2•5

(10)⁸ = (2•5)⁸ = 2⁸ • 5⁸

Equation at the end of step  3  :

   454                 3   
  (——— • (28•58)) ÷ ———————
   100              (26•56)

Step  4  :

            227
 Simplify   ———
            50 

Equation at the end of step  4  :

  227                 3   
  ——— • (28•58)) ÷ ———————
  50               (26•56)

Step  5  :

Dividing exponents :

 5.1    2⁸   divided by   2¹   = 2^{(8 - 1)} = 2⁷

Dividing exponents :

 5.2    5⁸   divided by   5²   = 5^{(8 - 2)} = 5⁶

Equation at the end of step  5  :

  6)3 
  ———————
  (26•56)

Step  6  :

                             3   
 Divide  (227•27•56)  by  ———————
                          (26•56)

Multiplying exponents :

 6.1    2⁷  multiplied by  2⁶   = 2^{(7 + 6)} = 2¹³

Multiplying exponents :

 6.2    5⁶  multiplied by  5⁶   = 5^{(6 + 6)} = 5¹²

Final result :

  (227•213•512)                                   
  ————————————— = 1.51333 • 1014 
        3