Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.5" was replaced by "(45/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  1  :

   54         45
  (——•(108))•(——•(25•55))
   10         10

Step  2  :

            9
 Simplify   —
            2

Equation at the end of step  2  :

   54             9
  (—— • (108)) • (— • (25•55))
   10             2

Step  3  :

Raising to a Power :

 3.1    2⁵   divided by   2¹   = 2^{(5 - 1)} = 2⁴

Equation at the end of step  3  :

   54
  (—— • (108)) • (32•24•55)
   10

Step  4  :

 4.1     10 = 2•5

(10)⁸ = (2•5)⁸ = 2⁸ • 5⁸

Equation at the end of step  4  :

   54
  (—— • (28•58)) • (32•24•55)
   10

Step  5  :

            27
 Simplify   ——
            5 

Equation at the end of step  5  :

   27
  (—— • (28•58)) • (32•24•55)
   5 

Step  6  :

Dividing exponents :

 6.1    5⁸   divided by   5¹   = 5^{(8 - 1)} = 5⁷

Equation at the end of step  6  :

  (33•28•57) • (32•24•55)

Step  7  :

Multiplying exponents :

 7.1    3³  multiplied by  3²   = 3^{(3 + 2)} = 3⁵

Multiplying exponents :

 7.2    2⁸  multiplied by  2⁴   = 2^{(8 + 4)} = 2¹²

Multiplying exponents :

 7.3    5⁷  multiplied by  5⁵   = 5^{(7 + 5)} = 5¹²

Final result :

  (35•212•512)