Multiply and Simplify: b^(-3) × b^3 × b^4 × b^(-2) Expression

Simplify the following expression:

$b^{-3}\times b^3\times b^4\times b^{-2}=$

When we need to calculate multiplication between terms with identical bases, we should use the appropriate exponent law:

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

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 obtain the following:

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

Here we applied the exponent law twice however we can also perform the same calculation for four or more terms in multiplication ..

Additionally, this law can only be used to calculate multiplication performed between terms with identical bases,

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

From here on we will no longer indicate the multiplication sign, instead we will place terms next to each other.

Let's return to the problem and apply the above law:

$b^{-3}b^3b^4b^{-2}=b^{-3+3+4-2}=b^2$

Therefore the correct answer is B.