Select the expression that is equivalent to (5x)^(-(1)/(2)) sqrt((5x)^(2)) (1)/(sqrt((5x)^(2))) sqrt(5x) (1)/(sqrt(5x))

Rephrase Question: We need to rephrase the question in one sentence.Analyze Given Expression: Let's analyze the given expression (5x)^(-(1)/(2)). The negative exponent means we take the reciprocal of the base, and the (1/2) exponent means we take the square root. So, (5x)^(-(1)/(2)) is equivalent to 1 over the square root of 5x.Check Options: Now let's check each option to see which one matches our analysis. The first option is sqrt((5x)^(2)). This is not equivalent because it represents the square root of (5x) squared, not the reciprocal of the square root of 5x.Option 1 Analysis: The second option is (1)/(sqrt((5x)^(2))). This option represents the reciprocal of the square root of (5x) squared, which simplifies to 1/(5x), not the reciprocal of the square root of 5x.Option 2 Analysis: The third option is sqrt(5x). This is not equivalent because it represents the square root of 5x, not the reciprocal of the square root of 5x.Option 3 Analysis: The fourth option is (1)/(sqrt(5x)). This option represents the reciprocal of the square root of 5x, which matches our analysis of the given expression (5x)^(-(1)/(2)).Option 4 Analysis: Therefore, the expression equivalent to (5x)^(-(1)/(2)) is (1)/(sqrt(5x)).

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Select the expression that is equivalent to
(5x)^(-(1)/(2))

sqrt((5x)^(2))

(1)/(sqrt((5x)^(2)))

sqrt(5x)

(1)/(sqrt(5x))

Select the expression that is equivalent to $(5 x)^{-\frac{1}{2}}$ $\newline$ $\sqrt{(5 x)^{2}}$ $\newline$ $\frac{1}{\sqrt{(5 x)^{2}}}$ $\newline$ $\sqrt{5 x}$ $\newline$ $\frac{1}{\sqrt{5 x}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

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Q. Select the expression that is equivalent to

(5 x)^{-\frac{1}{2}}

\newline

\sqrt{(5 x)^{2}}

\newline

\frac{1}{\sqrt{(5 x)^{2}}}

\newline

\sqrt{5 x}

\newline

\frac{1}{\sqrt{5 x}}

Rephrase Question: We need to rephrase the question in one sentence.
Analyze Given Expression: Let's analyze the given expression $(5x)^{-(1)/(2)}$ . The negative exponent means we take the reciprocal of the base, and the $(1/2)$ exponent means we take the square root. So, $(5x)^{-(1)/(2)}$ is equivalent to $1$ over the square root of $5x$ .
Check Options: Now let's check each option to see which one matches our analysis. $\newline$ The first option is $\sqrt{(5x)^{2}}$ . This is not equivalent because it represents the square root of $(5x)^{2}$ , not the reciprocal of the square root of $5x$ .
Option $1$ Analysis: The second option is $(1)/(\sqrt{(5x)^{2}})$ . This option represents the reciprocal of the square root of $(5x)^{2}$ , which simplifies to $1/(5x)$ , not the reciprocal of the square root of $5x$ .
Option $2$ Analysis: The third option is $\sqrt{5x}$ . This is not equivalent because it represents the square root of $5x$ , not the reciprocal of the square root of $5x$ .
Option $3$ Analysis: The fourth option is $(1)/(\sqrt{5x})$ . This option represents the reciprocal of the square root of $5x$ , which matches our analysis of the given expression $(5x)^{-(1)/(2)}$ .
Option $4$ Analysis: Therefore, the expression equivalent to $(5x)^{-(\frac{1}{2})}$ is $\frac{1}{\sqrt{5x}}$ .