Answer:
[tex]\frac{8x^{10}z}{y^{4}}[/tex]
Step-by-step explanation:
The expression [tex]\frac{(2x^{3}z^{2})^{3}}{x^{3} y^{4}z^{2}.x^{-4}z^{3}}[/tex]
Using laws of exponents
The law that
[tex]x^{m} x^{n} = x^{m+n}[/tex]
Solving in the denominator
[tex]\frac{(2x^{3}z^{2})^{3}}{x^{3} y^{4}z^{2}.x^{-4}z^{3}}=\frac{(2x^{3}z^{2})^{3}}{x^{3-4} y^{4}z^{2+3}}=\frac{(2x^{3}z^{2})^{3}}{x^{-1} y^{4}z^{5}}[/tex]
The law that
[tex](x^{m})^{n} =x^{mn}[/tex]
solving in the numerator
[tex]\frac{(2x^{3}z^{2})^{3}}{x^{-1} y^{4}z^{5}}=\frac{2x^{3.3}z^{2.3}}{x^{-1} y^{4}z^{5}}=\frac{2x^{9}z^{6}}{x^{-1} y^{4}z^{5}}[/tex]
The law that
[tex]\frac{x^{m}}{x^{n}} = x^{m-n}[/tex]
solving the fraction
[tex]\frac{2x^{9}z^{6}}{x^{-1} y^{4}z^{5}}=\frac{2x^{9-(-1)}z^{6-5}}{y^{4}}[/tex]
Resulting
[tex]\frac{8x^{10}z}{y^{4} }[/tex]
