Question

id="TexFormula1" title=" (\frac{2}{3} x^{-3} y^{4} z^{2})^{3} " alt=" (\frac{2}{3} x^{-3} y^{4} z^{2})^{3} " align="absmiddle" class="latex-formula"> 

Answer 1

$\bf ~~~~~~~~~~~~\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} \qquad \qquad \cfrac{1}{a^n}\implies a^{-n} \qquad \qquad a^n\implies \cfrac{1}{a^{-n}} \\\\ -------------------------------$

$\bf \left(\cfrac{2}{3}x^{-3}y^4z^2 \right)^3\implies \stackrel{\textit{distributing the exponent}}{\left[\left( \cfrac{2}{3} \right)^3x^{^{-3\cdot 3}}y^{4\cdot 3}z^{2\cdot 3} \right]}\implies \cfrac{2^3}{3^3}x^{-9}y^{12}z^6 \\\\\\ \cfrac{8}{27}\cdot \cfrac{1}{x^9}y^{12}z^6\implies \cfrac{8y^{12}z^6}{27x^9}$