( 10^(4/10) * 100^(8/10) ) / 100

asked by guest
on Nov 14, 2024 at 11:40 pm



You asked:

Evaluate the expression: \(\frac{{10}^{\frac{4}{10}} \cdot {100}^{\frac{8}{10}}}{100}\)

MathBot Answer:

\[\frac{{10}^{\frac{4}{10}} \cdot {100}^{\frac{8}{10}}}{100} = 1\]

\[\begin{aligned}\frac{{10}^{\frac{4}{10}} \cdot {100}^{\frac{8}{10}}}{100}& = 10^{\frac{4}{10}} \cdot 100^{\frac{8}{10}} \cdot \frac{1}{100}\\& = 10^{\frac{2}{5}} \cdot 100^{\frac{8}{10}} \cdot \frac{1}{100}\\& = 10^{\frac{2}{5}} \cdot 10 \cdot 10^{\frac{3}{5}} \cdot \frac{1}{100}\\& = 10^{\frac{2}{5}} \cdot \frac{1}{10} \cdot 10^{\frac{3}{5}}\\& = 1\end{aligned}\]

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