Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "8.5" was replaced by "(85/10)". 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  :

   17         85
  (——•(104))•(——•((2)(-2)•(5)(-2)))
   10         10

Step  2  :

            17
 Simplify   ——
            2 

Equation at the end of step  2  :

   17             17
  (—— • (104)) • (—— • ((2)(-2)•(5)(-2)))
   10             2 

Step  3  :

Raising to a Power :

 3.1    2¹  multiplied by  2²   = 2^{(1 + 2)} = 2³

Equation at the end of step  3  :

   17             17
  (—— • (104)) • ———
   10            200

Step  4  :

 4.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  4  :

   17               17
  (—— • (24•54)) • ———
   10              200

Step  5  :

            17
 Simplify   ——
            10

Equation at the end of step  5  :

   17               17
  (—— • (24•54)) • ———
   10              200

Step  6  :

Dividing exponents :

 6.1    2⁴   divided by   2¹   = 2^{(4 - 1)} = 2³

Dividing exponents :

 6.2    5⁴   divided by   5¹   = 5^{(4 - 1)} = 5³

Equation at the end of step  6  :

                17
  (17•23•53) • ———
               200

Step  7  :

Multiplying exponents :

 7.1    17¹  multiplied by  17¹   = 17^{(1 + 1)} = 17²

Canceling Out :

 7.2      Canceling out  2³ as it appears on both sides of the fraction line

Dividing exponents :

 7.3    5³   divided by   5²   = 5^{(3 - 2)} = 5¹ = 5

Final result :

  1445