To solve the exercise you can use these rules of exponents
[tex]\begin{gathered} a^m\cdot a^n=a^{m+n} \\ \text{and} \\ a^{-m}=\frac{1}{m} \end{gathered}[/tex]
So, in this case, you have
Using the first rule
[tex]4^4\cdot4^{-6}=4^{4-6}=4^{-2}[/tex]
Using the second rule
[tex]4^{-2}=\frac{1}{4^2}[/tex]
Then,
[tex]4^4\cdot4^{-6}=\frac{1}{4^2}[/tex]
Therefore, the expression equivalent to the given expression is
[tex]\frac{1}{4^2}[/tex]
and the correct answer is option a.
