Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.1" was replaced by "(41/10)".

Step  1  :

 1.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  1  :

   41
  (—— • (105)) • (22•52)
   10

Step  2  :

 2.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  2  :

   41
  (—— • (25•55)) • (22•52)
   10

Step  3  :

            41
 Simplify   ——
            10

Equation at the end of step  3  :

   41
  (—— • (25•55)) • (22•52)
   10

Step  4  :

Dividing exponents :

 4.1    2⁵   divided by   2¹   = 2^{(5 - 1)} = 2⁴

Dividing exponents :

 4.2    5⁵   divided by   5¹   = 5^{(5 - 1)} = 5⁴

Equation at the end of step  4  :

  (41•24•54) • (22•52)

Step  5  :

Multiplying exponents :

 5.1    2⁴  multiplied by  2²   = 2^{(4 + 2)} = 2⁶

Multiplying exponents :

 5.2    5⁴  multiplied by  5²   = 5^{(4 + 2)} = 5⁶

Final result :

  (41•26•56)