Answer
$$10x^{2}y^{4}$$
Work Step by Step
$$\frac{9y^4}{x^{-2}}+ (\frac{x^{-1}}{y^2})^{-2}$$
Simplify the first term: $\frac{9y^4}{x^{-2}}$
Recall the negative exponent rule: $a^{−n}=\frac{1}{a^{n}}$ and $\frac{1}{a^{-n}} = a^{n}$
Thus,
$$\frac{9y^4}{x^{-2}} = 9x^{2}y^{4}$$
Simplify the second term: $(\frac{x^{-1}}{y^2})^{-2}$
Recall the power rule: $(a^{m})^{n}=a^{mn}$
Thus,
$$(\frac{x^{-1}}{y^2})^{-2} = \frac{x^{-1\cdot-2}}{y^{2\cdot-2}} = \frac{x^{2}}{y^{-4}}$$
Recall the negative exponent rule: $a^{−n}=\frac{1}{a^{n}}$ and $\frac{1}{a^{-n}} = a^{n}$
Thus,
$$\frac{x^{2}}{y^{-4}} = x^{2}y^{4}$$
Rewrite the equation:
$$9x^{2}y^{4} + x^{2}y^{4} = 10x^{2}y^{4}$$
