2/(9(-0.1)^(4/3))

asked by guest
on Jan 23, 2025 at 5:32 pm



You asked:

Evaluate the expression: 29(−0.1)43\frac{2}{9 {\left( -0.1 \right)}^{\frac{4}{3}}}

MathBot Answer:

29(−0.1)43=20(−1)23⋅1039\frac{2}{9 {\left( -0.1 \right)}^{\frac{4}{3}}} = \frac{20 \left(-1\right)^{\frac{2}{3}} \cdot \sqrt[3]{10}}{9}

29(−0.1)43=2⋅19⋅(−110)43=2⋅19⋅(−110)43=2⋅19⋅(−110)43=2⋅19⋅−1100⋅−13⋅1023=2⋅1−9100⋅−13⋅1023=209⋅(−1)23⋅103\begin{aligned}\frac{2}{9 {\left( -0.1 \right)}^{\frac{4}{3}}}&=2 \cdot \frac{1}{9 \cdot \left(- \frac{1}{10}\right)^{\frac{4}{3}}}\\&=2 \cdot \frac{1}{9 \cdot \left(\frac{-1}{10}\right)^{\frac{4}{3}}}\\&=2 \cdot \frac{1}{9 \cdot \left(- \frac{1}{10}\right)^{\frac{4}{3}}}\\&=2 \cdot \frac{1}{9 \cdot - \frac{1}{100} \cdot \sqrt[3]{-1} \cdot 10^{\frac{2}{3}}}\\&=2 \cdot \frac{1}{- \frac{9}{100} \cdot \sqrt[3]{-1} \cdot 10^{\frac{2}{3}}}\\&=\frac{20}{9} \cdot \left(-1\right)^{\frac{2}{3}} \cdot \sqrt[3]{10}\end{aligned}

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