which expression is equivalent to $x^{-\frac{5}{3}}$?\n$\frac{1}{sqrt5{x^{3}}}$\n$\frac{1}{sqrt3{x^{5}}}$\n$…
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
Answer:
B. $\frac{1}{\sqrt[3]{x^{5}}}$
Explanation:
Step1: Recall negative - exponent rule
$a^{-n}=\frac{1}{a^{n}}$. So, $x^{-\frac{5}{3}}=\frac{1}{x^{\frac{5}{3}}}$.
Step2: Recall fractional - exponent rule
$a^{\frac{m}{n}}=\sqrt[n]{a^{m}}$. Then, $x^{\frac{5}{3}}=\sqrt[3]{x^{5}}$.
Step3: Combine results
$x^{-\frac{5}{3}}=\frac{1}{\sqrt[3]{x^{5}}}$.