which expression is equivalent to $x^{-\frac{5}{3}}$?\n$\\frac{1}{\\sqrt5{x^{3}}}$\n$\\frac{1}{\\sqrt3{x^{5}}…

which expression is equivalent to $x^{-\frac{5}{3}}$?\n$\\frac{1}{\\sqrt5{x^{3}}}$\n$\\frac{1}{\\sqrt3{x^{5}}}$\n$-\\sqrt3{x^{5}}$\n$-\\sqrt5{x^{3}}$

which expression is equivalent to $x^{-\frac{5}{3}}$?\n$\\frac{1}{\\sqrt5{x^{3}}}$\n$\\frac{1}{\\sqrt3{x^{5}}}$\n$-\\sqrt3{x^{5}}$\n$-\\sqrt5{x^{3}}$

Answer

Explanation:

Step1: Recall negative - exponent rule

By the rule $a^{-n}=\frac{1}{a^{n}}$, for $a = x$ and $n=\frac{5}{3}$, we have $x^{-\frac{5}{3}}=\frac{1}{x^{\frac{5}{3}}}$.

Step2: Recall fractional - exponent rule

The fractional - exponent rule states that $a^{\frac{m}{n}}=\sqrt[n]{a^{m}}$. So, $x^{\frac{5}{3}}=\sqrt[3]{x^{5}}$. Then $\frac{1}{x^{\frac{5}{3}}}=\frac{1}{\sqrt[3]{x^{5}}}$.

Answer:

$\frac{1}{\sqrt[3]{x^{5}}}$ (corresponding to the second option in the multiple - choice list)