Respuesta :
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.
The equivalent expression to x Superscript negative five-thirds is "StartFraction 1 Over RootIndex 3 StartRoot x Superscript 5 Baseline EndRoot EndFraction"
[tex] = \frac{1}{ \sqrt[3]{ {x}^{5} } } [/tex]
Given:
x Superscript negative five-thirds
[tex] = {x}^{ - \frac{5}{3} } [/tex]
[tex] = \frac{1}{ {x}^{ \frac{5}{3} } } [/tex]
[tex] = \frac{1}{ \sqrt[3]{ {x}^{5} } } [/tex]
Given options:
- 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
Therefore, the equivalent expression to x Superscript negative five-thirds is "StartFraction 1 Over RootIndex 3 StartRoot x Superscript 5 Baseline EndRoot EndFraction"
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