Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.2" was replaced by "(12/10)". 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  :

   54       12
  (——•(105))——•(22•52))
   10(      10

Step  2  :

            6
 Simplify   —
            5

Equation at the end of step  2  :

   54             6
  (—— • (105)) ÷ (— • (22•52))
   10             5

Step  3  :

Multiplying exponents :

 3.1    2¹  multiplied by  2²   = 2^{(1 + 2)} = 2³

Raising to a Power :

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

Equation at the end of step  3  :

   54
  (—— • (105)) ÷ 120
   10

Step  4  :

 4.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  4  :

   54
  (—— • (25•55)) ÷ 120
   10

Step  5  :

            27
 Simplify   ——
            5 

Equation at the end of step  5  :

  27
  —— • (25•55)) ÷ 120
  5 

Step  6  :

Dividing exponents :

 6.1    5⁵   divided by   5¹   = 5^{(5 - 1)} = 5⁴

Equation at the end of step  6  :

Step  7  :

            (33•25•54) 
 Simplify   ——————————
               120    

Dividing exponents :

 7.1    3³   divided by   3¹   = 3^{(3 - 1)} = 3²

Dividing exponents :

 7.2    2⁵   divided by   2³   = 2^{(5 - 3)} = 2²

Dividing exponents :

 7.3    5⁴   divided by   5¹   = 5^{(4 - 1)} = 5³

Final result :

  4500