Solution - Simplification or other simple results

Step  1  :

 1.1     10 = 2•5

(10)⁷ = (2•5)⁷ = 2⁷ • 5⁷

Equation at the end of step  1  :

  ((5 • (105)) • 5) • (27•57)

Step  2  :

 2.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  2  :

  ((5 • (25•55)) • 5) • (27•57)

Step  3  :

Multiplying exponents :

 3.1    5¹  multiplied by  5⁵   = 5^{(1 + 5)} = 5⁶

Equation at the end of step  3  :

  ((56•25) • 5) • (27•57)

Step  4  :

Multiplying exponents :

 4.1    5⁶  multiplied by  5¹   = 5^{(6 + 1)} = 5⁷

Equation at the end of step  4  :

  (57•25) • (27•57)

Step  5  :

Multiplying exponents :

 5.1    5⁷  multiplied by  5⁷   = 5^{(7 + 7)} = 5¹⁴

Multiplying exponents :

 5.2    2⁵  multiplied by  2⁷   = 2^{(5 + 7)} = 2¹²

Final result :

  (514•212)