Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-3" was replaced by "^(-3)".

Step  1  :

 1.1     10 = 2•5

(10)^-3 = (2•5)^(-3) = (2)^(-3) • (5)^(-3)

Equation at the end of step  1  :

  (4 • (106)) • (6 • ((2)(-3)•(5)(-3)))

Step  2  :

Raising to a Power :

 2.1    2¹   divided by   2³   = 2^{(1 - 3)} = 2^(-2) = ¹/_2²

Equation at the end of step  2  :

                 3 
  (4 • (106)) • ———
                500

Step  3  :

 3.1     10 = 2•5

(10)⁶ = (2•5)⁶ = 2⁶ • 5⁶

Equation at the end of step  3  :

                   3 
  (4 • (26•56)) • ———
                  500

Step  4  :

Multiplying exponents :

 4.1    2²  multiplied by  2⁶   = 2^{(2 + 6)} = 2⁸

Equation at the end of step  4  :

             3 
  (28•56) • ———
            500

Step  5  :

Dividing exponents :

 5.1    2⁸   divided by   2²   = 2^{(8 - 2)} = 2⁶

Dividing exponents :

 5.2    5⁶   divided by   5³   = 5^{(6 - 3)} = 5³

Final result :

  (26•53•3)