Answer: [tex]\dfrac{1}{16}x^{-5}y^{-2}z^{4}[/tex]
Step-by-step explanation:
Given
Expression is [tex]\left(4xy^3z^{-2}\right)^{-2}\cdot x^{-3}y^4z^0[/tex]
using the Exponent property that is
[tex][(a)^b]^c=a^{b\cdot c}\\a^x\cdot a^y=a^{x+y}[/tex]
Applying the above property
[tex]\Rightarrow \left(4xy^3z^{-2}\right)^{-2}\cdot x^{-3}y^4z^0=4^{-2}x^{-2}y^{-6}z^{4}\cdot x^{-3}y^4z^0\\\\\Rightarrow \left(4xy^3z^{-2}\right)^{-2}\cdot x^{-3}y^4z^0=4^{-2}x^{-2-3}y^{-6+4}z^{4+0}\\\Rightarrow 4^{-2}x^{-5}y^{-2}z^{4}=\dfrac{1}{16}x^{-5}y^{-2}z^{4}[/tex]