(1/6*10**22)^(1/6)

asked by guest
on Nov 16, 2024 at 9:23 pm



You asked:

Evaluate the expression: \({\left( \frac{1}{6} \cdot {10}^{22} \right)}^{\frac{1}{6}}\)

MathBot Answer:

\[{\left( \frac{1}{6} \cdot {10}^{22} \right)}^{\frac{1}{6}} = \frac{1000 \sqrt{2} \cdot 3^{\frac{5}{6}} \cdot 5^{\frac{2}{3}}}{3} \approx 3443.29943730818682629220554302361368\]

\[\begin{aligned}{\left( \frac{1}{6} \cdot {10}^{22} \right)}^{\frac{1}{6}}& = \sqrt[6]{\frac{1}{6} \cdot 10^{22}}\\& = \sqrt[6]{\frac{10000000000000000000000}{6}}\\& = \sqrt[6]{\frac{5000000000000000000000}{3}}\\& = \frac{1000}{3} \cdot \sqrt{2} \cdot 3^{\frac{5}{6}} \cdot 5^{\frac{2}{3}}\end{aligned}\]

+ Submit Question