[tex]\begin{gathered} \text{Multiplying powers with the same base:} \\ a^m\cdot a^n=a^{m+n} \\ \\ \text{Dividing powers with the same base:} \\ \frac{a^m}{a^n}=a^{m-n} \\ \\ \text{Power of power:} \\ (a^m)^n=a^{m\cdot n} \end{gathered}[/tex]
To get the given final answer using the three rules above you can create the next expression:
[tex]-\frac{3y^3}{5y^2x^2x(z^2)^2}[/tex]
To solve it:
Use dividing powers with the same base to simplify the base y:
[tex]-\frac{3y^{3-2}}{5x^2x(z^2)^2}=-\frac{3y^{}}{5^{}x^2x(z^2)^2}[/tex]
Use multipliying powers with the same base to simplify the base x.
[tex]-\frac{3y^{}}{5^{}x^{2+1}(z^2)^2}=\frac{3y^{}}{5^{}x^3(z^2)^2}[/tex]
Use power of a power to simplify z:
[tex]-\frac{3y^{}}{5x^3(z^{2\cdot2})}=-\frac{3y^{}}{5x^3z^4}[/tex]
