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  :

  (4 • (105)) • (2 • (25•55))

Step  2  :

Raising to a Power :

 2.1    2¹  multiplied by  2⁵   = 2^{(1 + 5)} = 2⁶

Equation at the end of step  2  :

  (4 • (105)) • (26•55)

Step  3  :

 3.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  3  :

  (4 • (25•55)) • (26•55)

Step  4  :

Multiplying exponents :

 4.1    2²  multiplied by  2⁵   = 2^{(2 + 5)} = 2⁷

Equation at the end of step  4  :

  (27•55) • (26•55)

Step  5  :

Multiplying exponents :

 5.1    2⁷  multiplied by  2⁶   = 2^{(7 + 6)} = 2¹³

Multiplying exponents :

 5.2    5⁵  multiplied by  5⁵   = 5^{(5 + 5)} = 5¹⁰

Final result :

  (213•510)