which is equivalent to $80^{\frac{1}{4}x}$?\n$\\left(\\frac{80}{4}\\right)^x$\n$\\sqrt4{80^x}$\n$\\sqrtx{80^4…

which is equivalent to $80^{\frac{1}{4}x}$?\n$\\left(\\frac{80}{4}\\right)^x$\n$\\sqrt4{80^x}$\n$\\sqrtx{80^4}$\n$\\left(\\frac{80}{x}\\right)^4$

which is equivalent to $80^{\frac{1}{4}x}$?\n$\\left(\\frac{80}{4}\\right)^x$\n$\\sqrt4{80^x}$\n$\\sqrtx{80^4}$\n$\\left(\\frac{80}{x}\\right)^4$

Answer

Explanation:

Step1: Recall exponent - root relationship

The expression (a^{\frac{m}{n}}=\sqrt[n]{a^{m}}). Here, we have (80^{\frac{1}{4}x}), which can be rewritten using the power - of - a - power rule ((a^{m})^{n}=a^{mn}). First, rewrite (80^{\frac{1}{4}x}) as ((80^{\frac{1}{4}})^{x}). And by the definition of the (n)th - root, (a^{\frac{1}{n}}=\sqrt[n]{a}), so (80^{\frac{1}{4}}=\sqrt[4]{80}). Then ((80^{\frac{1}{4}})^{x}=(\sqrt[4]{80})^{x}=\sqrt[4]{80^{x}}).

Answer:

(\sqrt[4]{80^{x}}) (the second option)