Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-2" was replaced by "^(-2)".

(2): "5.8" was replaced by "(58/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   16       58
  (——•(107))——•((2)(-2)•(5)(-2)))
   10(      10

Step  2  :

            29
 Simplify   ——
            5 

Equation at the end of step  2  :

   16             29
  (—— • (107)) ÷ (—— • ((2)(-2)•(5)(-2)))
   10             5 

Step  3  :

Raising to a Power :

 3.1    5¹  multiplied by  5²   = 5^{(1 + 2)} = 5³

Equation at the end of step  3  :

   16             29
  (—— • (107)) ÷ ———
   10            500

Step  4  :

 4.1     10 = 2•5

(10)⁷ = (2•5)⁷ = 2⁷ • 5⁷

Equation at the end of step  4  :

   16               29
  (—— • (27•57)) ÷ ———
   10              500

Step  5  :

            8
 Simplify   —
            5

Equation at the end of step  5  :

  8               29
  — • (27•57)) ÷ ———
  5              500

Step  6  :

Multiplying exponents :

 6.1    2³  multiplied by  2⁷   = 2^{(3 + 7)} = 2¹⁰

Dividing exponents :

 6.2    5⁷   divided by   5¹   = 5^{(7 - 1)} = 5⁶

Equation at the end of step  6  :

  )29
  ———
  500

Step  7  :

                        29
 Divide  (210•56)  by  ———
                       500

Multiplying exponents :

 7.1    2¹⁰  multiplied by  2²   = 2^{(10 + 2)} = 2¹²

Multiplying exponents :

 7.2    5⁶  multiplied by  5³   = 5^{(6 + 3)} = 5⁹

Final result :

  (212•59)                                  
  ———————— = 2.75862 • 108 
     29