\left(-\frac{1}{27}\right)^{-\frac{2}{3}}+\left(-\frac{1}{32}\right)^{-\frac{2}{5}}

asked by guest
on Nov 19, 2024 at 7:30 pm



You asked:

Evaluate the expression: (−(127))−(23)+(−(132))−(25){\left( -\left( \frac{1}{27} \right) \right)}^{-\left( \frac{2}{3} \right)} + {\left( -\left( \frac{1}{32} \right) \right)}^{-\left( \frac{2}{5} \right)}

MathBot Answer:

(−(127))−(23)+(−(132))−(25)=−9−13−4(−1)35{\left( -\left( \frac{1}{27} \right) \right)}^{-\left( \frac{2}{3} \right)} + {\left( -\left( \frac{1}{32} \right) \right)}^{-\left( \frac{2}{5} \right)} = - 9 \sqrt[3]{-1} - 4 \left(-1\right)^{\frac{3}{5}}

(−(127))−(23)+(−(132))−(25)=1(−127)23+1(−132)25=−9⋅−13+1(−132)25=−9⋅−13−4⋅(−1)35\begin{aligned}{\left( -\left( \frac{1}{27} \right) \right)}^{-\left( \frac{2}{3} \right)} + {\left( -\left( \frac{1}{32} \right) \right)}^{-\left( \frac{2}{5} \right)}&=\frac{1}{\left(- \frac{1}{27}\right)^{\frac{2}{3}}} + \frac{1}{\left(- \frac{1}{32}\right)^{\frac{2}{5}}}\\&=-9 \cdot \sqrt[3]{-1} + \frac{1}{\left(- \frac{1}{32}\right)^{\frac{2}{5}}}\\&=-9 \cdot \sqrt[3]{-1} - 4 \cdot \left(-1\right)^{\frac{3}{5}}\end{aligned}

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