Simplify (5×12×4×6) Raised to Power (a+3bx): Complex Base Exponents

While 1440 is mathematically correct, the question asks you to simplify using exponent rules. Computing the product loses the individual prime factors, making it harder to factor or simplify further in more complex problems.

Yes! When you have $(a\cdot b\cdot c\cdot d)^n$, the exponent n applies to each factor separately: $a^n \cdot b^n \cdot c^n \cdot d^n$.

The same rule applies! $(5\cdot12\cdot4\cdot6)^3 = 5^3 \cdot 12^3 \cdot 4^3 \cdot 6^3$. Whether the exponent is a number or an algebraic expression like a+3bx, you distribute it to each factor.

Absolutely! You could factor $12 = 2^2 \cdot 3$ and $4 = 2^2$ and $6 = 2 \cdot 3$ for even more simplification, but the question only asks for the basic power rule application.

This form shows the structure of the expression clearly. Each base factor keeps its exponent, making it easier to see patterns, combine like terms, or apply additional algebraic operations later.