Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "8.2" was replaced by "(82/10)".

Step  1  :

 1.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  1  :

                  82
  (4 • (105)) +  (—— • (22•52))
                  10

Step  2  :

            41
 Simplify   ——
            5 

Equation at the end of step  2  :

                  41
  (4 • (105)) +  (—— • (22•52))
                  5 

Step  3  :

Raising to a Power :

 3.1    5²   divided by   5¹   = 5^{(2 - 1)} = 5¹ = 5

Equation at the end of step  3  :

  (4 • (105)) +  820

Step  4  :

 4.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  4  :

  (4 • (25•55)) +  820

Step  5  :

Multiplying exponents :

 5.1    2²  multiplied by  2⁵   = 2^{(2 + 5)} = 2⁷

Equation at the end of step  5  :

  (27•55) +  820

Step  6  :

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   2⁷ • 5⁵ + 820  =   4 • (1 + 205) 

Final result :

  4 • (1 + 205)