Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-4" was replaced by "^(-4)". 1 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

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

Step  2  :

 2.1     10 = 2•5

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

Equation at the end of step  2  :

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

Step  3  :

Dividing exponents :

 3.1    2¹   divided by   2²   = 2^{(1 - 2)} = 2^(-1) = ¹/_2¹ = ¹/₂

Equation at the end of step  3  :

    1
  (—— • 5) • ((2)(-4)•(5)(-4))
   50

Step  4  :

Multiplying exponents :

 4.1    2¹  multiplied by  2⁴   = 2^{(1 + 4)} = 2⁵

Multiplying exponents :

 4.2    5¹  multiplied by  5⁴   = 5^{(1 + 4)} = 5⁵

Final result :

     1                                      
  ——————— = 10.00000 • 10-6 
  (25•55)