which is equivalent to $sqrt{10^{\frac{3}{4}x}}$?\n$(sqrt3{10})^{4x}$\n$(sqrt4{10})^{3x}$\n$(sqrt6{10})^{4x}$…

which is equivalent to $sqrt{10^{\frac{3}{4}x}}$?\n$(sqrt3{10})^{4x}$\n$(sqrt4{10})^{3x}$\n$(sqrt6{10})^{4x}$\n$(sqrt8{10})^{3x}$

which is equivalent to $sqrt{10^{\frac{3}{4}x}}$?\n$(sqrt3{10})^{4x}$\n$(sqrt4{10})^{3x}$\n$(sqrt6{10})^{4x}$\n$(sqrt8{10})^{3x}$

Answer

Explanation:

Step1: Recall exponent - radical conversion rule

We know that $a^{\frac{m}{n}}=\sqrt[n]{a^{m}}$. Given $10^{\frac{3}{4}x}$, we can rewrite it using the rule. First, rewrite the exponent as $\frac{3x}{4}$. Then, by the rule $a^{\frac{m}{n}}=\sqrt[n]{a^{m}}$, we have $10^{\frac{3x}{4}}=\sqrt[4]{10^{3x}}=(\sqrt[4]{10})^{3x}$.

Answer:

$(\sqrt[4]{10})^{3x}$ (the second option)