Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.5" was replaced by "(25/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)⁹ = (2•5)⁹ = 2⁹ • 5⁹

Equation at the end of step  1  :

   11         25
  (——•(103))•(——•(29•59))
   10         10

Step  2  :

            5
 Simplify   —
            2

Equation at the end of step  2  :

   11             5
  (—— • (103)) • (— • (29•59))
   10             2

Step  3  :

Multiplying exponents :

 3.1    5¹  multiplied by  5⁹   = 5^{(1 + 9)} = 5¹⁰

Raising to a Power :

 3.2    2⁹   divided by   2¹   = 2^{(9 - 1)} = 2⁸

Equation at the end of step  3  :

   11
  (—— • (103)) • (510•28)
   10

Step  4  :

 4.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  4  :

   11
  (—— • (23•53)) • (510•28)
   10

Step  5  :

            11
 Simplify   ——
            10

Equation at the end of step  5  :

   11
  (—— • (23•53)) • (510•28)
   10

Step  6  :

Dividing exponents :

 6.1    2³   divided by   2¹   = 2^{(3 - 1)} = 2²

Dividing exponents :

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

Equation at the end of step  6  :

  1100 • (510•28)

Step  7  :

Multiplying exponents :

 7.1    2²  multiplied by  2⁸   = 2^{(2 + 8)} = 2¹⁰

Multiplying exponents :

 7.2    5²  multiplied by  5¹⁰   = 5^{(2 + 10)} = 5¹²

Final result :

  (210•512•11)