Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "1.17" was replaced by "(117/100)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

  2    117
  — • (——— • ((2)(-4)•(5)(-4)))
  3    100

Step  2  :

            117
 Simplify   ———
            100

Equation at the end of step  2  :

  2    117
  — • (——— • ((2)(-4)•(5)(-4)))
  3    100

Step  3  :

Multiplying exponents :

 3.1    2²  multiplied by  2⁴   = 2^{(2 + 4)} = 2⁶

Multiplying exponents :

 3.2    5²  multiplied by  5⁴   = 5^{(2 + 4)} = 5⁶

Equation at the end of step  3  :

  2     117  
  — • ———————
  3   (26•56)

Step  4  :

            2
 Simplify   —
            3

Equation at the end of step  4  :

  2     117  
  — • ———————
  3   (26•56)

Step  5  :

Dividing exponents :

 5.1    2¹   divided by   2⁶   = 2^{(1 - 6)} = 2^(-5) = ¹/_2⁵

Dividing exponents :

 5.2    3²   divided by   3¹   = 3^{(2 - 1)} = 3¹ = 3

Final result :

     39             
  ——————— = 0.00008 
  (25•56)