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

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



You asked:

Evaluate the expression: (16⋅1022)16{\left( \frac{1}{6} \cdot {10}^{22} \right)}^{\frac{1}{6}}

MathBot Answer:

(16⋅1022)16=10002⋅356⋅5233≈3443.29943730818682629220554302361368{\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

(16⋅1022)16=16⋅10226=1000000000000000000000066=500000000000000000000036=10003⋅2⋅356⋅523\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}

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