The rules of exponents tell you to add exponents in the numerator and subtract those in the denominator. A power of a power causes the exponent to be multiplied.
[tex]\dfrac{(2x^{3}z^{2})^{3}}{x^{3}y^{4}z^2x^{-4}z^{3}}=2^{3}x^{(3\cdot3-3-(-4))}y^{-4}z^{(2\cdot3-2-3)}\\\\=\dfrac{8x^{10}z}{y^{4}}[/tex]
