Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-5" was replaced by "^(-5)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

  ((4 • (10-3)) • -5) • ((2)(-5)•(5)(-5))

Step  2  :

 2.1     10 = 2•5

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

Equation at the end of step  2  :

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

Step  3  :

Dividing exponents :

 3.1    2²   divided by   2³   = 2^{(2 - 3)} = 2^(-1) = ¹/_2¹ = ¹/₂

Equation at the end of step  3  :

    1 
  (——— • -5) • ((2)(-5)•(5)(-5))
   250

Step  4  :

Multiplying exponents :

 4.1    2¹  multiplied by  2⁵   = 2^{(1 + 5)} = 2⁶

Multiplying exponents :

 4.2    5²  multiplied by  5⁵   = 5^{(2 + 5)} = 5⁷

Final result :

     -1                                     
  ——————— = -2.00000 • 10-7 
  (26•57)