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

which shows the following expression after the negative exponents have been eliminated?\n\\(\\frac{xy^{-6}}{x^{-4}y^{2}},x\\neq0,y\\neq0\\)\n\\(\\frac{x^{4}}{y^{2}x^{6}y^{6}}\\)\n\\(\\frac{xx^{4}}{y^{2}y^{6}}\\)\n\\(\\frac{x^{4}}{y^{2}xy^{6}}\\)\n\\(\\frac{x^{4}y^{2}}{xy^{6}}\\)

which shows the following expression after the negative exponents have been eliminated?\n\\(\\frac{xy^{-6}}{x^{-4}y^{2}},x\\neq0,y\\neq0\\)\n\\(\\frac{x^{4}}{y^{2}x^{6}y^{6}}\\)\n\\(\\frac{xx^{4}}{y^{2}y^{6}}\\)\n\\(\\frac{x^{4}}{y^{2}xy^{6}}\\)\n\\(\\frac{x^{4}y^{2}}{xy^{6}}\\)

Answer

Explanation:

Step1: Apply 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 using the rule. The $x^{-4}$ in the denominator moves to the numerator as $x^{4}$ and the $y^{-6}$ in the numerator moves to the denominator as $y^{6}$. So we get $\frac{x\times x^{4}}{y^{2}\times y^{6}}$.

Step2: Use product - of - powers rule

The product - of - powers rule states that $a^{m}\times a^{n}=a^{m + n}$. Here, $x\times x^{4}=x^{1 + 4}=x^{5}$, but the form $\frac{x\times x^{4}}{y^{2}\times y^{6}}$ is also a correct form after eliminating negative exponents.

Answer:

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