# arrow_back Given $y=\sqrt{x^{7}}-\frac{5}{x^{3}}$ Which of the following is equivalent to $y$ ?

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Given
$y=\sqrt{x^{7}}-\frac{5}{x^{3}}$
Which of the following is equivalent to $y$ ?

\begin{align}
\begin{array}{|l|l|}
\hline \text { A } & x^{14}-5 x^{-3} \\
\hline \text { B } & x^{\frac{7}{2}}+5 x^{-3} \\
\hline \text { C } & x^{\frac{7}{2}}-5 x^{-3} \\
\hline \text { D } & x^{\frac{7}{2}}-5 x^{\frac{1}{3}} \\
\hline
\end{array}
\end{align}

Identify the correct expression for $y$
Looking at the first term:
\begin{aligned} y_{1} &=\sqrt{x^{7}} \\ &=\left(x^{7}\right)^{\frac{1}{2}} \\ &=x^{\frac{7}{2}} \end{aligned}
And then looking at the second term:
\begin{aligned} y_{2} &=-\frac{5}{x^{3}} \\ &=-5 x^{-3} \end{aligned}
Putting these together gives us:
\begin{aligned} y &=y_{1}+y_{2} \\ &=x^{\frac{7}{2}}-5 x^{-3} \end{aligned}
So the correct choice is Option $\mathbf{C}$.
by Platinum
(104,456 points)

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