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)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  1  :

                 41
  ((2 • (102)) • ——) • (25•55)
                 10

Step  2  :

            41
 Simplify   ——
            10

Equation at the end of step  2  :

                 41
  ((2 • (102)) • ——) • (25•55)
                 10

Step  3  :

 3.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  3  :

                   41
  ((2 • (22•52)) • ——) • (25•55)
                   10

Step  4  :

Multiplying exponents :

 4.1    2¹  multiplied by  2²   = 2^{(1 + 2)} = 2³

Equation at the end of step  4  :

             41
  ((23•52) • ——) • (25•55)
             10

Step  5  :

Dividing exponents :

 5.1    2³   divided by   2¹   = 2^{(3 - 1)} = 2²

Dividing exponents :

 5.2    5²   divided by   5¹   = 5^{(2 - 1)} = 5¹ = 5

Equation at the end of step  5  :

  820 • (25•55)

Step  6  :

Multiplying exponents :

 6.1    2²  multiplied by  2⁵   = 2^{(2 + 5)} = 2⁷

Multiplying exponents :

 6.2    5¹  multiplied by  5⁵   = 5^{(1 + 5)} = 5⁶

Final result :

  (27•56•41)