Answer
$\dfrac{y^{10}}{49x^4}$
Work Step by Step
RECALL:
(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:
$=7^{-2}(x^{2})^{-2}(y^{-5})^{-2}$
Use the power rule to find:
$=7^{-2}x^{2(-2)}y^{-5(-2)}
\\=7^{-2}x^{-4}y^{10}$
Use the negative-exponent rule to find:
$=\dfrac{1}{7^2}\cdot \dfrac{1}{x^{4}} \cdot y^{10}
\\=\dfrac{1}{49} \cdot \dfrac{1}{x^4} \cdot y^{10}
\\=\dfrac{y^{10}}{49x^4}$
