Question

Simplify (5x^7y^3z^-1)^2x(2xy^-5)^3x(2y^-3z^2)^3

Answer 1

Remember
$(abc)^x=(a^x)(b^x)(c^x)$
and
$(x^m)(x^n)=x^{m+n}$
and
$(x^m)^n=x^{mn}$
and
$x^{-m}= \frac{1}{x^m}$
so

$(5x^7y^3z^{-1})^2(2xy^{-5})^3(2y^{-3}z^2)^3$=
$(5^2)((x^7)^2)((y^3)^2)((z^{-1})^2)(2^3)(x^3)((y^{-5})^3)(2^3)((y^{-3})^3)((z^2)^3)$=
$(25)(x^{14})(y^6)(z^{-2})(8)(x^3)(y^{-15})(8)(y^{-9})(z^6)$=
$1600x^{17}y^{-18}z^4$=
$\frac{1600x^{17}z^4}{y^{18}}$