Answer:
[tex]\huge \boxed{ \frac{x^{15} y^{25}}{z^{21} } }[/tex]
Step-by-step explanation:
[tex](x^2 y^3 z^{-3})^7 (xy^4)[/tex]
[tex]\sf Apply \ exponent \ rule : (a^b)^c=a^{bc}[/tex]
[tex](x^{2 \times 7} y^{3 \times 7} z^{-3 \times 7})(xy^4)[/tex]
[tex](x^{14} y^{21} z^{-21})(xy^4)[/tex]
[tex]x^{14} \times y^{21} \times z^{-21} \times x \times y^4[/tex]
[tex]\sf Apply \ exponent \ rule : a^b \times a^c=a^{b+c}[/tex]
[tex]x^{14} \times x^1 \times y^{21} \times y^4 \times z^{-21}[/tex]
[tex]x^{14+1} \times y^{21+4} \times z^{-21}[/tex]
[tex]x^{15} \times y^{25} \times z^{-21}[/tex]
[tex]\displaystyle \sf Apply \ exponent \ rule : a^{-b} =\frac{1}{a^b}[/tex]
[tex]\displaystyle x^{15} \times y^{25} \times \frac{1}{z^{21} }[/tex]
[tex]\displaystyle \frac{x^{15} y^{25}}{z^{21} }[/tex]
