(3*2^-52)^(1/3)

asked by guest
on Sep 21, 2024 at 1:16 pm



You asked:

Evaluate the expression: \({\left( 3 \cdot {2}^{-52} \right)}^{\frac{1}{3}}\)

MathBot Answer:

\[{\left( 3 \cdot {2}^{-52} \right)}^{\frac{1}{3}} = \frac{2^{\frac{2}{3}} \cdot \sqrt[3]{3}}{262144}\]

\[\begin{aligned}{\left( 3 \cdot {2}^{-52} \right)}^{\frac{1}{3}}& = \sqrt[3]{3 \cdot \frac{1}{2^{52}}}\\& = \sqrt[3]{\frac{3}{4503599627370496}}\\& = \frac{1}{262144} \cdot 2^{\frac{2}{3}} \cdot \sqrt[3]{3}\end{aligned}\]

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