Answer
$\dfrac{25y^8}{49x^{10}}$
Work Step by Step
(i) $a^{-m} = \dfrac{1}{a^m}, a\ne0$
(ii) $(ab)^m=a^mb^m$
(iii) $(a^m)^n=a^{mn}$
Use the rules above to obtain:
$=\dfrac{1}{\left(-\dfrac{7x^5}{5y^4}\right)^2}$
The negative sign goes away since we are raising everything to an even power.
$\\=\dfrac{1}{\left(\dfrac{7^2(x^5)^2}{5^2(y^4)^2}\right)}
\\=\dfrac{1}{\left(\dfrac{49x^{2\cdot5}}{25y^{4\cdot2}}\right)}
\\=\dfrac{1}{\left(\dfrac{49x^{10}}{25y^{8}}\right)}
\\=1 \cdot \dfrac{25y^8}{49x^{10}}
\\=\dfrac{25y^8}{49x^{10}}$
