0.25^-3.5

asked by guest
on Nov 27, 2024 at 1:59 am



You asked:

Evaluate the expression: \({0.25}^{-3.5}\)

MathBot Answer:

\[{0.25}^{-3.5} = 128\]

\[\begin{aligned}{0.25}^{-3.5}& = \left(\frac{25}{100}\right)^{- \left(3 + \frac{5}{10}\right)}\\& = \left(\frac{1}{4}\right)^{- \left(3 + \frac{5}{10}\right)}\\& = \left(\frac{1}{4}\right)^{- \left(3 + \frac{1}{2}\right)}\\& = \left(\frac{1}{4}\right)^{- \frac{7}{2}}\\& = \frac{1}{(\frac{1}{4})^{7/2}}\\& = 128\end{aligned}\]

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