Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-4" was replaced by "^(-4)".

(2): "2.857" was replaced by "(2857/1000)".

Step  1  :

 1.1     10 = 2•5

(10)^-4 = (2•5)^(-4) = (2)^(-4) • (5)^(-4)

Equation at the end of step  1  :

                   2857
  ((12 • (1010)) • ————) • ((2)(-4)•(5)(-4))
                   1000

Step  2  :

            2857
 Simplify   ————
            1000

Equation at the end of step  2  :

                   2857
  ((12 • (1010)) • ————) • ((2)(-4)•(5)(-4))
                   1000

Step  3  :

 3.1     10 = 2•5

(10)¹⁰ = (2•5)¹⁰ = 2¹⁰ • 5¹⁰

Equation at the end of step  3  :

                      2857
  ((12 • (210•510)) • ————) • ((2)(-4)•(5)(-4))
                      1000

Step  4  :

Multiplying exponents :

 4.1    2²  multiplied by  2¹⁰   = 2^{(2 + 10)} = 2¹²

Equation at the end of step  4  :

                 2857
  ((212•3•510) • ————) • ((2)(-4)•(5)(-4))
                 1000

Step  5  :

Dividing exponents :

 5.1    2¹²   divided by   2³   = 2^{(12 - 3)} = 2⁹

Dividing exponents :

 5.2    5¹⁰   divided by   5³   = 5^{(10 - 3)} = 5⁷

Equation at the end of step  5  :

  (29•3•57•2857) • ((2)(-4)•(5)(-4))

Step  6  :

Dividing exponents :

 6.1    2⁹   divided by   2⁴   = 2^{(9 - 4)} = 2⁵

Dividing exponents :

 6.2    5⁷   divided by   5⁴   = 5^{(7 - 4)} = 5³

Final result :

  (25•3•53•2857)