Question

which shows the following expression after the negative exponents have been eliminated? (\frac{xy^{-6}}{x^{-4}y^2}, x
eq0,y
eq0)

Explanation:

Step1: Rewrite negative exponents

Recall $a^{-n}=\frac{1}{a^n}$. So:
$$\frac{xy^{-8}}{x^{-4}y^2} = \frac{x \cdot \frac{1}{y^8}}{\frac{1}{x^4} \cdot y^2}$$

Step2: Simplify complex fraction

Dividing by a fraction is multiplying by its reciprocal:
$$\frac{x}{y^8} \cdot \frac{x^4}{y^2} = \frac{x \cdot x^4}{y^8 \cdot y^2}$$

Step3: Combine like bases

Use $a^m \cdot a^n = a^{m+n}$:
$$\frac{x^{1+4}}{y^{8+2}} = \frac{x^5}{y^{10}}$$
(Note: Matching the option format, this is equivalent to $\frac{x^5}{y^2 y^8}$, which aligns with the first option $\frac{x^5}{y^2 y^8}$ written as $\frac{x^5}{y^2 y^8}$ or $\frac{x^5}{y^{10}}$)

Answer:

$\frac{x^5}{y^2 y^8}$ (or simplified as $\frac{x^5}{y^{10}}$)