Show two different methods for simplifying an expression. Which method do you prefer and why?

Question

Expression is: (3x²Y³)³

Answer 1

Perhaps it should not, yet another (and maybe more) method exists:

(3x²y³)³

(3x²y³)(3x²y³)(3x²y³)                   definition of exponentiation

3 · 3 · 3 x^{2 ·} x^2 · x^2 · y^3 · y³ · y³    commutative property of multiplication

27 x⁶ y⁹                                       multiplication and law of exponents

Answer 2

The outermost exponent, 3, should multiply the exponent of each factor of the parenthesized monomial.

 

3³•x⁶•y⁹;  final answer:   27x⁶y⁹

 

There really should not be any other method!