(12^1/3)×(81^-1/6)×(162^1/3)
You asked:
Evaluate the expression: \(\frac{{12}^{1}}{3} \cdot \frac{{81}^{-1}}{6} \cdot \frac{{162}^{1}}{3}\)
MathBot Answer:
\[\frac{{12}^{1}}{3} \cdot \frac{{81}^{-1}}{6} \cdot \frac{{162}^{1}}{3} = \frac{4}{9} = 0.\overline{4}\]
\[\begin{aligned}\frac{{12}^{1}}{3} \cdot \frac{{81}^{-1}}{6} \cdot \frac{{162}^{1}}{3}& = 12^{1} \cdot \frac{1}{3} \cdot \frac{1}{81} \cdot \frac{1}{6} \cdot 162^{1} \cdot \frac{1}{3}\\& = \frac{12}{3} \cdot \frac{1}{81} \cdot \frac{1}{6} \cdot 162^{1} \cdot \frac{1}{3}\\& = \frac{12}{3} \cdot \frac{1}{81} \cdot \frac{162}{6} \cdot \frac{1}{3}\\& = \frac{12}{3} \cdot \frac{1}{81} \cdot \frac{54}{6}\\& = \frac{4}{81} \cdot \frac{54}{6}\\& = \frac{2}{243} \cdot 54\\& = \frac{4}{9}\end{aligned}\]