Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.4" was replaced by "(24/10)". 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  :

   41         24
  (——•(105))•(——•(22•52))
   10         10

Step  2  :

            12
 Simplify   ——
            5 

Equation at the end of step  2  :

   41             12
  (—— • (105)) • (—— • (22•52))
   10             5 

Step  3  :

Multiplying exponents :

 3.1    2²  multiplied by  2²   = 2^{(2 + 2)} = 2⁴

Raising to a Power :

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

Equation at the end of step  3  :

   41
  (—— • (105)) • 240
   10

Step  4  :

 4.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  4  :

   41
  (—— • (25•55)) • 240
   10

Step  5  :

            41
 Simplify   ——
            10

Equation at the end of step  5  :

   41
  (—— • (25•55)) • 240
   10

Step  6  :

Dividing exponents :

 6.1    2⁵   divided by   2¹   = 2^{(5 - 1)} = 2⁴

Dividing exponents :

 6.2    5⁵   divided by   5¹   = 5^{(5 - 1)} = 5⁴

Equation at the end of step  6  :

  (41•24•54) • 240

Step  7  :

Multiplying exponents :

 7.1    2⁴  multiplied by  2⁴   = 2^{(4 + 4)} = 2⁸

Multiplying exponents :

 7.2    5⁴  multiplied by  5¹   = 5^{(4 + 1)} = 5⁵

Final result :

  (41•28•55•3)