Answer
$\dfrac{y^{7}}{x^{13}z^{2}}$
Work Step by Step
Use the laws of exponents to simplify the given expression, $
\dfrac{x^{-6}y^3z^{-1}}{x^7y^{-4}z}
.$
Using the Quotient Rule of the laws of exponents which states that $\dfrac{x^m}{x^n}=x^{m-n},$ the quotient of the expression above is
\begin{array}{l}\require{cancel}
x^{-6-7}y^{3-(-4)}z^{-1-1}
\\\\=
x^{-6-7}y^{3+4}z^{-1-1}
\\\\=
x^{-13}y^{7}z^{-2}
.\end{array}
Using the Negative Exponent Rule of the laws of exponents which states that $x^{-m}=\dfrac{1}{x^m}$ or $\dfrac{1}{x^{-m}}=x^m,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{y^{7}}{x^{13}z^{2}}
.\end{array}