Simplify the Expression: c^(-1)·d^6·d^(-2)·c^3·c^2 Using Laws of Exponents

We will use the power rule for multiplying terms with identical bases:

$a^m\cdot a^n=a^{m+n}$

Let's emphasize that this rule is valid only for terms with identical bases,

Here in the problem there are also terms with negative exponents, but this doesn't pose an issue regarding the use of the aforementioned power rule. In fact, this power rule is valid in all cases for numerical terms with different powers, including negative powers, rational number powers, and even irrational number powers, etc.

Let's return to the problem,

Let's note that there are two types of terms in the problem that differ from each other with different bases. First, for good order, we'll use the commutative law of multiplication to arrange the expression so that all terms with the same base are adjacent, let's get to work:

$c^{-1}\cdot d^6\cdot d^{-2}\cdot c^3\cdot c^2=c^{-1}\cdot c^3\cdot c^2\cdot d^6\cdot d^{-2}$

Then we'll apply the aforementioned power rule separately to each different type of term,

$c^{-1}\cdot c^3\cdot c^2\cdot d^6\cdot d^{-2}=c^{-1+3+2}\cdot d^{6+(-2)}=c^{-1+3+2}\cdot d^{6-2}=c^4\cdot d^4$

$$When we actually applied the mentioned rule separately - for terms with base $c$and for terms with base $d$ and combined the powers in the exponent when we grouped all terms with the same base together.

Therefore, the correct answer is B.