Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "8.1" was replaced by "(81/10)".

Step  1  :

 1.1     10 = 2•5

(10)^-1 = (2•5)^(-1) = (2)^(-1) • (5)^(-1)

Equation at the end of step  1  :

                  81
  (2 • (10-4)) • (—— • ((2)(-1)•(5)(-1)))
                  10

Step  2  :

            81
 Simplify   ——
            10

Equation at the end of step  2  :

                  81
  (2 • (10-4)) • (—— • ((2)(-1)•(5)(-1)))
                  10

Step  3  :

Multiplying exponents :

 3.1    2¹  multiplied by  2¹   = 2^{(1 + 1)} = 2²

Raising to a Power :

 3.2    5¹  multiplied by  5¹   = 5^{(1 + 1)} = 5²

Equation at the end of step  3  :

                  81
  (2 • (10-4)) • ———
                 100

Step  4  :

 4.1     10 = 2•5

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

Equation at the end of step  4  :

                             81
  (2 • ((2)(-4)•(5)(-4))) • ———
                            100

Step  5  :

Dividing exponents :

 5.1    2¹   divided by   2⁴   = 2^{(1 - 4)} = 2^(-3) = ¹/_2³

Equation at the end of step  5  :

    1     81
  ———— • ———
  5000   100

Step  6  :

Final result :

    81             
  —————— = 0.00016 
  500000