Solve: (5×6×4)^x × 3^x × 4^y Exponential Expression

Solve the following problem:

$(5\times6\times4)^x\times3^x\times4^y=$

Begin by calculating the result of the multiplication inside of the parentheses in the first term of the multiplication and proceed to write down the entire expression:

$(5\cdot6\cdot4)^x\cdot3^x\cdot4^y=120^x\cdot3^x\cdot4^y$
Note that the first two terms in the multiplication have the same exponent, hence we can apply the law of exponents for parentheses, however in the opposite direction:

$z^n\cdot t^n=(z\cdot t)^n$
This means that instead of opening the parentheses whilst applying the (same) exponent to each term of the multiplication inside the parentheses. We'll place the two terms (with identical exponents) as a multiplication inside of the parentheses under the exponent. This is possible in this problem given that the first two terms in the multiplication have identical exponents,

Let's apply it to the problem:

$120^x\cdot3^x\cdot4^y =(120\cdot3)^x\cdot4^y$
Now we can of course calculate the result of the multiplication inside the parentheses if we want, and simplify the resulting expression even further, but at this stage it's worth noting that this result is answer A, and there is no other answer among the options that is both correct and more simplified,

Therefore, the correct answer is A.