Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "8.6" was replaced by "(86/10)". 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  :

   47         86
  (——•(108))•(——•((2)(-2)•(5)(-2)))
   10         10

Step  2  :

            43
 Simplify   ——
            5 

Equation at the end of step  2  :

   47             43
  (—— • (108)) • (—— • ((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  :

   47             43
  (—— • (108)) • ———
   10            500

Step  4  :

 4.1     10 = 2•5

(10)⁸ = (2•5)⁸ = 2⁸ • 5⁸

Equation at the end of step  4  :

   47               43
  (—— • (28•58)) • ———
   10              500

Step  5  :

            47
 Simplify   ——
            10

Equation at the end of step  5  :

   47               43
  (—— • (28•58)) • ———
   10              500

Step  6  :

Dividing exponents :

 6.1    2⁸   divided by   2¹   = 2^{(8 - 1)} = 2⁷

Dividing exponents :

 6.2    5⁸   divided by   5¹   = 5^{(8 - 1)} = 5⁷

Equation at the end of step  6  :

                43
  (47•27•57) • ———
               500

Step  7  :

Dividing exponents :

 7.1    2⁷   divided by   2²   = 2^{(7 - 2)} = 2⁵

Dividing exponents :

 7.2    5⁷   divided by   5³   = 5^{(7 - 3)} = 5⁴

Final result :

  (47•25•54•43)