Answer
Option (d)
Work Step by Step
RECALL:
A negative exponent means reciprocal.
Thus, $a^{-m} = \frac{1}{a^m}=(\frac{1}{a})^m$.
Using the rule above gives:
$(\frac{y^2}{x^3})^{-2}=(\frac{x^3}{y^2})^2$
Simplify using the rule $(a^m)^n=a^{mn}$ to obtain:
$=\dfrac{x^{3(2)}}{y^{2(2)}}
\\=\dfrac{x^6}{y^4}$
Thus, the answer is Option (d).