$0.04^{-1.5}$

asked by guest
on Jun 03, 2023 at 4:34 am

You asked:

Evaluate the expression: \({0.04}^{-1.5}\)

MathBot Answer:

\[{0.04}^{-1.5} = 125\]

\[\begin{aligned}{0.04}^{-1.5}& = \left(\frac{4}{100}\right)^{- \left(1 + \frac{5}{10}\right)}\\& = \left(\frac{1}{25}\right)^{- \left(1 + \frac{5}{10}\right)}\\& = \left(\frac{1}{25}\right)^{- \left(1 + \frac{1}{2}\right)}\\& = \left(\frac{1}{25}\right)^{- \frac{3}{2}}\\& = \frac{1}{(\frac{1}{25})^{3/2}}\\& = 125\end{aligned}\]

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