((-2)÷5)^(-2)×((-4)÷5)^4

asked by guest
on Nov 29, 2024 at 6:48 pm



You asked:

Evaluate the expression: \({\left( \frac{-2}{5} \right)}^{-2} {\left( \frac{-4}{5} \right)}^{4}\)

MathBot Answer:

\[{\left( \frac{-2}{5} \right)}^{-2} {\left( \frac{-4}{5} \right)}^{4} = \frac{64}{25} = 2.56\]


\[\begin{aligned}{\left( \frac{-2}{5} \right)}^{-2} {\left( \frac{-4}{5} \right)}^{4}& = \frac{1}{\left(- \frac{2}{5}\right)^{2}} \cdot \left(- \frac{4}{5}\right)^{4}\\& = \frac{25}{4} \cdot \left(- \frac{4}{5}\right)^{4}\\& = \frac{25}{4} \cdot \frac{256}{625}\\& = \frac{64}{25}\end{aligned}\]