Which expression is equivalent to x Superscript negative five-thirds? StartFraction 1 Over RootIndex 5 StartRoot x cubed EndRoot EndFraction StartFraction 1 Over RootIndex 3 StartRoot x Superscript 5 Baseline EndRoot EndFraction Negative RootIndex 3 StartRoot x Superscript 5 Baseline EndRoot Negative RootIndex 5 StartRoot x cubed EndRoot

Option B : [tex]\frac{1}{\sqrt[3]{x^{5} } }[/tex] is the expression equivalent to [tex]x^{-\frac{5}{3}[/tex]Explanation:The given expression is [tex]x^{-\frac{5}{3}[/tex]Rewriting the expression [tex]x^{-\frac{5}{3}[/tex] using the exponent rule, [tex]$a^{-b}=\frac{1}{a^{b}}$[/tex]Hence, we get,[tex]\frac{1}{x^{\frac{5}{3} } }[/tex]Simplifying, we get,[tex]\frac{1}{\left(x^{5}\right)^{\frac{1}{3}}}[/tex]Applying the rule, [tex]a^{\frac{1}{n}}=\sqrt[n]{a}[/tex]Thus, we have,[tex]\frac{1}{\sqrt[3]{x^{5} } }[/tex]Now, we shall determine from the options that which expression is equivalent to [tex]x^{-\frac{5}{3}[/tex]Option A: [tex]\frac{1}{\sqrt[5]{x^{3} } }[/tex]The expression [tex]\frac{1}{\sqrt[5]{x^{3} } }[/tex] is not equivalent to simplified expression  [tex]\frac{1}{\sqrt[3]{x^{5} } }[/tex]Thus, the expression [tex]\frac{1}{\sqrt[5]{x^{3} } }[/tex] is not equivalent to [tex]x^{-\frac{5}{3}[/tex]Hence, Option A is not the correct answer.Option B: [tex]\frac{1}{\sqrt[3]{x^{5} } }[/tex]The expression [tex]\frac{1}{\sqrt[3]{x^{5} } }[/tex] is equivalent to the simplified expression  [tex]\frac{1}{\sqrt[3]{x^{5} } }[/tex]Thus, the expression [tex]\frac{1}{\sqrt[3]{x^{5} } }[/tex] is equivalent to [tex]x^{-\frac{5}{3}[/tex]Hence, Option B is the correct answer.Option C: [tex]-\sqrt[3]{x^5}[/tex]The expression [tex]-\sqrt[3]{x^5}[/tex] is not equivalent to the simplified expression [tex]\frac{1}{\sqrt[3]{x^{5} } }[/tex]Thus, the expression [tex]-\sqrt[3]{x^5}[/tex] is not equivalent to [tex]x^{-\frac{5}{3}[/tex]Hence, Option C is not the correct answer.Option D: [tex]-\sqrt[5]{x^3}[/tex]The expression [tex]-\sqrt[5]{x^3}[/tex] is not equivalent to the simplified expression [tex]\frac{1}{\sqrt[3]{x^{5} } }[/tex]Thus, the expression [tex]-\sqrt[5]{x^3}[/tex] is not equivalent to [tex]x^{-\frac{5}{3}[/tex]Hence, Option D is not the correct answer.