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

MathBot Answer:

\[{\left( -\left( \frac{1}{27} \right) \right)}^{-\left( \frac{2}{3} \right)} + {\left( -\left( \frac{1}{32} \right) \right)}^{-\left( \frac{2}{5} \right)} = - 9 \sqrt[3]{-1} - 4 \left(-1\right)^{\frac{3}{5}}\]

\[\begin{aligned}{\left( -\left( \frac{1}{27} \right) \right)}^{-\left( \frac{2}{3} \right)} + {\left( -\left( \frac{1}{32} \right) \right)}^{-\left( \frac{2}{5} \right)}& = \frac{1}{\left(- \frac{1}{27}\right)^{\frac{2}{3}}} + \frac{1}{\left(- \frac{1}{32}\right)^{\frac{2}{5}}}\\& = -9 \cdot \sqrt[3]{-1} + \frac{1}{\left(- \frac{1}{32}\right)^{\frac{2}{5}}}\\& = -9 \cdot \sqrt[3]{-1} - 4 \cdot \left(-1\right)^{\frac{3}{5}}\end{aligned}\]

+ Submit Question