Question

select the expression that is equivalent to \\(\frac{1}{(5x)^{\frac{1}{2}}}\\)

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

Explanation:

Step1: Recall the exponent rule $a^{\frac{1}{n}}=\sqrt[n]{a}$

For the expression $\frac{1}{(5x)^{\frac{1}{2}}}$, using the rule $a^{\frac{1}{n}}=\sqrt[n]{a}$, we know that $(5x)^{\frac{1}{2}}=\sqrt{5x}$.

Step2: Substitute the equivalent form

Substituting $(5x)^{\frac{1}{2}}=\sqrt{5x}$ into the original expression $\frac{1}{(5x)^{\frac{1}{2}}}$, we get $\frac{1}{\sqrt{5x}}$.

Answer:

$\frac{1}{\sqrt{5x}}$ (the last option)