Solution - Simplification or other simple results

Step  1  :

 1.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  1  :

  (3 • (109)) • (2 • (24•54))

Step  2  :

Raising to a Power :

 2.1    2¹  multiplied by  2⁴   = 2^{(1 + 4)} = 2⁵

Equation at the end of step  2  :

  (3 • (109)) • (25•54)

Step  3  :

 3.1     10 = 2•5

(10)⁹ = (2•5)⁹ = 2⁹ • 5⁹

Equation at the end of step  3  :

  (3 • (29•59)) • (25•54)

Step  4  :

Equation at the end of step  4  :

  (3•29•59) • (25•54)

Step  5  :

Multiplying exponents :

 5.1    2⁹  multiplied by  2⁵   = 2^{(9 + 5)} = 2¹⁴

Multiplying exponents :

 5.2    5⁹  multiplied by  5⁴   = 5^{(9 + 4)} = 5¹³

Final result :

  (3•214•513)