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Select the expression that is equivalent to
2x^(-(1)/(2))

(2)/(sqrt(x^(2)))

(1)/(sqrt(2x^(2)))

(1)/(sqrt(2x))

(2)/(sqrtx)

Select the expression that is equivalent to $2 x^{-\frac{1}{2}}$ $\newline$ $\frac{2}{\sqrt{x^{2}}}$ $\newline$ $\frac{1}{\sqrt{2 x^{2}}}$ $\newline$ $\frac{1}{\sqrt{2 x}}$ $\newline$ $\frac{2}{\sqrt{x}}$

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Simplify radical expressions with root inside the root

Full solution

Q. Select the expression that is equivalent to

2 x^{-\frac{1}{2}}

\newline

\frac{2}{\sqrt{x^{2}}}

\newline

\frac{1}{\sqrt{2 x^{2}}}

\newline

\frac{1}{\sqrt{2 x}}

\newline

\frac{2}{\sqrt{x}}

Understand given expression: First, let's understand the given expression $2x^{-(1)/(2)}$ . The negative exponent indicates that the term is in the denominator, and the $(1/2)$ exponent indicates a square root. So, we can rewrite the expression as: $\newline$ $2 \times (x^{-1/2})$ $\newline$ = $2 / (x^{1/2})$ $\newline$ = $2 / \sqrt{x}$
Rewrite expression: Now, let's compare the rewritten expression with the given options: $\newline$ $(2)/(\sqrt{x^{2}})$ - This is not equivalent because $\sqrt{x^2}$ simplifies to $|x|$ , not $\sqrt{x}$ . $\newline$ $(1)/(\sqrt{2x^{2}})$ - This is not equivalent because $\sqrt{2x^2}$ simplifies to $\sqrt{2}\cdot|x|$ , not $\sqrt{x}$ . $\newline$ $(1)/(\sqrt{2x})$ - This is not equivalent because there is a missing factor of $2$ in the numerator. $\newline$ $\sqrt{x^2}$ $0$ - This matches our rewritten expression $\sqrt{x^2}$ $1$ .

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