Answer
$\dfrac{y^{8}}{25x^6}$
Work Step by Step
(i) The products-to-powers rule states that: $(ab)^n=a^nb^n$
(ii) The power rule states that: $(a^m)^n=a^{mn}$
(iii) The negative-exponent rule states that: $a^{-m} = \dfrac{1}{a^m}$ and $\dfrac{1}{a^{-m}} = a^m$
Use the products-to-powers rule to find:
$=5^{-2}(x^{3})^{-2}(y^{-4})^{-2}$
Use the power rule to find:
$=5^{-2}x^{3(-2)}y^{-4(-2)}
\\=5^{-2}x^{-6}y^{8}$
Use the negative-exponent rule to find:
$=\dfrac{1}{5^2}\cdot \dfrac{1}{x^{6}} \cdot y^{8}
\\=\dfrac{1}{25} \cdot \dfrac{1}{x^6} \cdot y^{8}
\\=\dfrac{y^{8}}{25x^6}$
