Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.9" was replaced by "(19/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  1  :

   45         19
  (——•(107))•(——•(24•54))
   10         10

Step  2  :

            19
 Simplify   ——
            10

Equation at the end of step  2  :

   45             19
  (—— • (107)) • (—— • (24•54))
   10             10

Step  3  :

Dividing exponents :

 3.1    2⁴   divided by   2¹   = 2^{(4 - 1)} = 2³

Raising to a Power :

 3.2    5⁴   divided by   5¹   = 5^{(4 - 1)} = 5³

Equation at the end of step  3  :

   45
  (—— • (107)) • (19•23•53)
   10

Step  4  :

 4.1     10 = 2•5

(10)⁷ = (2•5)⁷ = 2⁷ • 5⁷

Equation at the end of step  4  :

   45
  (—— • (27•57)) • (19•23•53)
   10

Step  5  :

            9
 Simplify   —
            2

Equation at the end of step  5  :

   9
  (— • (27•57)) • (19•23•53)
   2

Step  6  :

Dividing exponents :

 6.1    2⁷   divided by   2¹   = 2^{(7 - 1)} = 2⁶

Equation at the end of step  6  :

  (32•26•57) • (19•23•53)

Step  7  :

Multiplying exponents :

 7.1    2⁶  multiplied by  2³   = 2^{(6 + 3)} = 2⁹

Multiplying exponents :

 7.2    5⁷  multiplied by  5³   = 5^{(7 + 3)} = 5¹⁰

Final result :

  (32•29•510•19)