Answer:
B
Step-by-step explanation:
We need to understand 2 rules of exponents before simplifying this:
1. [tex](ab)^n = a^n*b^n[/tex]
2. [tex]a^{-n}=\frac{1}{a^n}[/tex]
Lets use the first property to simplify this:
[tex](4a^3b^{-2})^{2}\\=(4)^2*(a^3)^2*(b^{-2})^2[/tex]
Now, we can use the property [tex](a^n)^b=a^{nb}[/tex] to further simplify:
[tex](4)^2*(a^3)^2*(b^{-2})^2\\=16a^6b^{-4}[/tex]
We like to keep exponents "positive", so we use property #2 shown above and write:
[tex]16a^6b^{-4}\\=\frac{16a^6}{b^4}[/tex]
So, the correct answer is B
