Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.45" was replaced by "(145/100)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)¹² = (2•5)¹² = 2¹² • 5¹²

Equation at the end of step  1  :

   12         145
  (——•(103))•(———•(212•512))
   10         100

Step  2  :

            29
 Simplify   ——
            20

Equation at the end of step  2  :

   12             29
  (—— • (103)) • (—— • (212•512))
   10             20

Step  3  :

Dividing exponents :

 3.1    2¹²   divided by   2²   = 2^{(12 - 2)} = 2¹⁰

Raising to a Power :

 3.2    5¹²   divided by   5¹   = 5^{(12 - 1)} = 5¹¹

Equation at the end of step  3  :

   12
  (—— • (103)) • (29•210•511)
   10

Step  4  :

 4.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  4  :

   12
  (—— • (23•53)) • (29•210•511)
   10

Step  5  :

            6
 Simplify   —
            5

Equation at the end of step  5  :

   6
  (— • (23•53)) • (29•210•511)
   5

Step  6  :

Multiplying exponents :

 6.1    2¹  multiplied by  2³   = 2^{(1 + 3)} = 2⁴

Dividing exponents :

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

Equation at the end of step  6  :

  1200 • (29•210•511)

Step  7  :

Multiplying exponents :

 7.1    2⁴  multiplied by  2¹⁰   = 2^{(4 + 10)} = 2¹⁴

Multiplying exponents :

 7.2    5²  multiplied by  5¹¹   = 5^{(2 + 11)} = 5¹³

Final result :

  (214•3•513•29)