When you multiply two powers of the same base, you sum the exponents:
[tex] a^b\cdot a^c = a^{b+c} [/tex]
So, in this case,
[tex] 4^4\cdot 4^{-9} = 4^{4-9} = 4^{-5} [/tex]
Now, negative exponents works like positive exponents, except you have to invert the number: i.e.
[tex] a^{-b} = \dfrac{1}{a^b} [/tex]
So, you have
[tex] 4^{-5} = \dfrac{1}{4^5} [/tex]
