Answer
$\dfrac{1}{4x^6y^{14}}$
Work Step by Step
RECALL:
(i) $(a^m)^n=a^{mn}$
(ii) $a^{-m} = \dfrac{1}{a^m}, a\ne0$
Use the rules above to have:
$=2^{-2}(x^3)^{-2}(y^7)^{-2}
\\=\dfrac{1}{2^2} \cdot x^{3(-2)} \cdot y^{7(-2)}
\\=\dfrac{1}{4} \cdot x^{-6} \cdot y^{-14}
\\=\dfrac{1}{4} \cdot \dfrac{1}{x^6} \cdot \dfrac{1}{y^{14}}
\\=\dfrac{1}{4x^6y^{14}}$