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))2) • (5 • ((2)(-3)•(5)(-3)))

Step  2  :

Raising to a Power :

 2.1    5¹   divided by   5³   = 5^{(1 - 3)} = 5^(-2) = ¹/_5²

Equation at the end of step  2  :

                    1 
  ((4 • (106))2) • ———
                   200

Step  3  :

 3.1     10 = 2•5

(10)⁶ = (2•5)⁶ = 2⁶ • 5⁶

Equation at the end of step  3  :

                      1 
  ((4 • (26•56))2) • ———
                     200

Step  4  :

Multiplying exponents :

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

Equation at the end of step  4  :

                1 
  ((28•56)2) • ———
               200
 Step  5  :

Dividing exponents :

 5.1    2¹⁶   divided by   2³   = 2^{(16 - 3)} = 2¹³

Dividing exponents :

 5.2    5¹²   divided by   5²   = 5^{(12 - 2)} = 5¹⁰

Final result :

  (213•510)