Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{\frac{1}{\sqrt[3]{\frac{1}{343}}}+{(\frac{1}{8})}^{-\frac{1}{3}}}{\sqrt[18\sqrt{144)]{}}}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{\frac{1}{\frac{1}{\sqrt[3]{343}}}+{(\frac{1}{8})}^{-\frac{1}{3}}}{\sqrt[18\sqrt{144)]{}}}\]
Calculate.
\[\frac{\frac{1}{\frac{1}{7}}+{(\frac{1}{8})}^{-\frac{1}{3}}}{\sqrt[18\sqrt{144)]{}}}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{\frac{1}{\frac{1}{7}}+\frac{1}{\sqrt[3]{\frac{1}{8}}}}{\sqrt[18\sqrt{144)]{}}}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{\frac{1}{\frac{1}{7}}+\frac{1}{\frac{1}{\sqrt[3]{8}}}}{\sqrt[18\sqrt{144)]{}}}\]
Calculate.
\[\frac{\frac{1}{\frac{1}{7}}+\frac{1}{\frac{1}{2}}}{\sqrt[18\sqrt{144)]{}}}\]
Invert and multiply.
\[\frac{7+\frac{1}{\frac{1}{2}}}{\sqrt[18\sqrt{144)]{}}}\]
Invert and multiply.
\[\frac{7+2}{\sqrt[18\sqrt{144)]{}}}\]
Simplify \(7+2\) to \(9\).
\[\frac{9}{\sqrt[18\sqrt{144)]{}}}\]
Since \(12\times 12=144\), the square root of \(144\) is \(12\).
\[\frac{9}{\sqrt[18\times 12]{3}}\]
Simplify \(18\times 12\) to \(216\).
\[\frac{9}{\sqrt[216]{3}}\]
Decimal Form: 8.954341
9/3^(1/216)
