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)⁷ = (2•5)⁷ = 2⁷ • 5⁷

Equation at the end of step  1  :

    54        12
  ((——•(103))•——)•(27•57)
    10        10

Step  2  :

            6
 Simplify   —
            5

Equation at the end of step  2  :

    54            6
  ((—— • (103)) • —) • (27•57)
    10            5

Step  3  :

 3.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  3  :

    54              6
  ((—— • (23•53)) • —) • (27•57)
    10              5

Step  4  :

            27
 Simplify   ——
            5 

Equation at the end of step  4  :

    27              6
  ((—— • (23•53)) • —) • (27•57)
    5               5

Step  5  :

Dividing exponents :

 5.1    5³   divided by   5¹   = 5^{(3 - 1)} = 5²

Equation at the end of step  5  :

          6
  (5400 • —) • (27•57)
          5

Step  6  :

Multiplying exponents :

 6.1    2⁴  multiplied by  2⁷   = 2^{(4 + 7)} = 2¹¹

Multiplying exponents :

 6.2    5¹  multiplied by  5⁷   = 5^{(1 + 7)} = 5⁸

Final result :

  (211•34•58)