Simplify the Expression: a^7 × (abc)^3 × a^4 Using Exponent Rules

First, let's carefully open the parentheses, using the law of exponents that applies to parentheses containing multiplication of terms:

$(z\cdot y)^n=z^n\cdot y^n$
which essentially states that when there is an exponent acting on parentheses containing multiplication between terms, when opening the parentheses the exponent will apply separately to each of the multiplication terms inside the parentheses.

Let's return to the problem and first deal with the term containing parentheses in the overall multiplication separately-

$(abc)^3=a^3\cdot b^3\cdot c^3$
when we opened the parentheses using the law of exponents mentioned above, so that when opening the parentheses we applied the exponent to each of the multiplication terms inside the parentheses.

Let's return to the problem, we got:

$a^7\cdot(abc)^3\cdot a^4=a^7\cdot a^3\cdot b^3\cdot c^3\cdot a^4$
From here on we will no longer indicate the multiplication sign, but use the conventional writing form where placing terms next to each other means multiplication.

Now let's arrange the expression by bases while using the multiplication commutative law:

$a^7a^3b^3c^3a^4=a^7a^3a^4b^3c^3$
We'll continue and simplify the expression by using the law of exponents for multiplication between terms with identical bases:

$y^m\cdot y^n=y^{m+n}$
Note that this law is valid for any number of terms in multiplication and not just for two terms, for example for multiplication of three terms with the same base we get:

$y^m\cdot y^n\cdot y^k=y^{m+n}\cdot y^k=y^{m+n+k}$
when we used the above law of exponents twice, we can also perform the same calculation for four terms in multiplication and so on...

Let's apply this law to the problem:

$a^7a^3a^4b^3c^3=a^{7+3+4}b^3c^3=a^{14}b^3c^3$
when we used the above law of exponents, for multiplication between terms with identical bases only for terms with the same base.

We got the most simplified expression, so we're done.

Therefore the correct answer is D.