Solution - Simplification or other simple results

Step  1  :

 1.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  1  :

  (108) • (25•55)

Step  2  :

 2.1     10 = 2•5

(10)⁸ = (2•5)⁸ = 2⁸ • 5⁸

Equation at the end of step  2  :

  (28•58) • (25•55)

Step  3  :

Multiplying exponents :

 3.1    2⁸  multiplied by  2⁵   = 2^{(8 + 5)} = 2¹³

Multiplying exponents :

 3.2    5⁸  multiplied by  5⁵   = 5^{(8 + 5)} = 5¹³

Final result :

  (213•513)