Question

which expression is equivalent to \\(x^{-\frac{5}{3}}\\)?

options:

1. \\(\frac{1}{\sqrt3{x^5}}\\)
2. \\(-\sqrt5{x^3}\\)
3. \\(\frac{1}{\sqrt5{x^3}}\\)
4. \\(-\sqrt3{x^5}\\)

Explanation:

Apply the negative exponent rule

$$ x^{-\frac{5}{3}} = \frac{1}{x^{\frac{5}{3}}} $$

Apply the fractional exponent rule

$$ x^{\frac{5}{3}} = \sqrt[3]{x^5} $$

Combine the simplified terms

$$ x^{-\frac{5}{3}} = \frac{1}{\sqrt[3]{x^5}} $$

Answer:

• (A) \(\frac{1}{\sqrt[5]{x^3}}\)
• (B) \(-\sqrt[5]{x^3}\)
• (C) \(\frac{1}{\sqrt[3]{x^5}}\) (Correct answer)
• (D) \(-\sqrt[3]{x^5}\)