(2/3)^ 4*(2/3)^-4

asked by guest
on Sep 26, 2024 at 9:18 pm



You asked:

Evaluate the expression: \({\left( \frac{2}{3} \right)}^{4} \cdot {\left( \frac{2}{3} \right)}^{-4}\)

MathBot Answer:

\[{\left( \frac{2}{3} \right)}^{4} \cdot {\left( \frac{2}{3} \right)}^{-4} = 1\]

\[\begin{aligned}{\left( \frac{2}{3} \right)}^{4} \cdot {\left( \frac{2}{3} \right)}^{-4}& = \left(\frac{2}{3}\right)^{4} \cdot \frac{1}{\left(\frac{2}{3}\right)^{4}}\\& = \frac{16}{81} \cdot \frac{1}{\left(\frac{2}{3}\right)^{4}}\\& = \frac{16}{81} \cdot \frac{81}{16}\\& = 1\end{aligned}\]

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