Solution - Simplification or other simple results

Step  1  :

 1.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  1  :

  (8 • (101)) • (1 • (22•52))

Step  2  :

 2.1     10 = 2•5

(10)¹ = (2•5)¹ = 2 • 5

Equation at the end of step  2  :

  (8 • (2•5)) • (22•52)

Step  3  :

Multiplying exponents :

 3.1    2³  multiplied by  2¹   = 2^{(3 + 1)} = 2⁴

Equation at the end of step  3  :

  (24•5) • (22•52)

Step  4  :

Multiplying exponents :

 4.1    2⁴  multiplied by  2²   = 2^{(4 + 2)} = 2⁶

Multiplying exponents :

 4.2    5¹  multiplied by  5²   = 5^{(1 + 2)} = 5³

Final result :

  (26•53)