$10^{-5.2}$

asked by guest
on Oct 27, 2024 at 12:28 pm



You asked:

Evaluate the expression: \({10}^{-5.2}\)

MathBot Answer:

\[{10}^{-5.2} = \frac{10^{\frac{4}{5}}}{1000000} \approx 0.00000630957344480193249434360137\]

\[\begin{aligned}{10}^{-5.2}& = 10^{- \left(5 + \frac{2}{10}\right)}\\& = 10^{- \left(5 + \frac{1}{5}\right)}\\& = 10^{- \frac{26}{5}}\\& = \frac{1}{10^{\frac{26}{5}}}\\& = \frac{1}{1000000} \cdot 10^{\frac{4}{5}}\end{aligned}\]

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