Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "6.7" was replaced by "(67/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  1  :

   96         67
  (——•(103))•(——•(22•52))
   10         10

Step  2  :

            67
 Simplify   ——
            10

Equation at the end of step  2  :

   96             67
  (—— • (103)) • (—— • (22•52))
   10             10

Step  3  :

Dividing exponents :

 3.1    2²   divided by   2¹   = 2^{(2 - 1)} = 2¹ = 2

Raising to a Power :

 3.2    5²   divided by   5¹   = 5^{(2 - 1)} = 5¹ = 5

Equation at the end of step  3  :

   96
  (—— • (103)) • 670
   10

Step  4  :

 4.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  4  :

   96
  (—— • (23•53)) • 670
   10

Step  5  :

            48
 Simplify   ——
            5 

Equation at the end of step  5  :

   48
  (—— • (23•53)) • 670
   5 

Step  6  :

Multiplying exponents :

 6.1    2⁴  multiplied by  2³   = 2^{(4 + 3)} = 2⁷

Dividing exponents :

 6.2    5³   divided by   5¹   = 5^{(3 - 1)} = 5²

Equation at the end of step  6  :

  9600 • 670

Step  7  :

Final result :

  6432000