Simplify. \[ \left(\frac{3 y^{5}}{z^{-6}}\right)^{-3} \] Write your answer using only positive exponents.

To simplify the expression \(\left(\frac{3 y^{5}}{z^{-6}}\right)^{-3}\), we start by applying the property of exponents that states \((a/b)^{-n} = (b/a)^{n}\). Thus, we can rewrite our expression: \[ \left(\frac{3 y^{5}}{z^{-6}}\right)^{-3} = \left(\frac{z^{-6}}{3 y^{5}}\right)^{3} \] Next, we need to distribute the exponent of 3 to both the numerator and the denominator: \[ = \frac{(z^{-6})^{3}}{(3 y^{5})^{3}} = \frac{z^{-18}}{27 y^{15}} \] Now we rewrite \(z^{-18}\) as \(\frac{1}{z^{18}}\): \[ = \frac{1}{27 y^{15} z^{18}} \] To express the entire expression with only positive exponents, we take the reciprocal of the fraction: \[ = \frac{z^{18}}{27 y^{15}} \] So the final simplified form with only positive exponents is: \[ \frac{z^{18}}{27 y^{15}} \]