which shows the following expression after the negative exponents have been eliminated?\n$\frac{xy^{-6}}{x^{…

Explanation:

Step1: Use negative - exponent rule

Recall that $a^{-n}=\frac{1}{a^{n}}$ and $\frac{1}{a^{-n}} = a^{n}$. For the given expression $\frac{xy^{-6}}{x^{-4}y^{2}}$, we can rewrite it as $xy^{-6}\times x^{4}y^{- 2}$ since $\frac{1}{x^{-4}}=x^{4}$ and $\frac{1}{y^{2}} = y^{-2}$.

Step2: Use product - rule of exponents

The product - rule states that $a^{m}\times a^{n}=a^{m + n}$. So, $xy^{-6}\times x^{4}y^{-2}=x^{1 + 4}y^{-6+( - 2)}=x^{5}y^{-8}$.

Step3: Eliminate negative exponents

Using the negative - exponent rule again, $y^{-8}=\frac{1}{y^{8}}$, and $x^{5}y^{-8}=\frac{x^{5}}{y^{8}}$. Another way is to directly rewrite the original expression: $\frac{xy^{-6}}{x^{-4}y^{2}}=\frac{x\times x^{4}}{y^{2}\times y^{6}}=\frac{x^{1 + 4}}{y^{2+6}}=\frac{x^{5}}{y^{8}}$. Among the given options, if we rewrite $\frac{xx^{4}}{y^{2}y^{6}}$, using the product - rule $a^{m}\times a^{n}=a^{m + n}$, we have $\frac{x^{1+4}}{y^{2 + 6}}=\frac{x^{5}}{y^{8}}$.

Answer:

$\frac{xx^{4}}{y^{2}y^{6}}$