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Question
if \[x = \left( \frac{3}{2} \right)^2 \times \left( \frac{2}{3} \right)^{- 4}\], find the value of x−2.
Solution
First, we have to find x.
\[x = \left( \frac{3}{2} \right)^2 \times \left( \frac{2}{3} \right)^{- 4} \]
\[ = \left( \frac{3}{2} \right)^2 \times \left( \frac{3}{2} \right)^4 \]
\[ = \left( \frac{3}{2} \right)^6\] →(a−1 = 1/a)
Hence, x−2 is:
\[x^{- 2} = \left( \left( \frac{3}{2} \right)^6 \right)^{- 2} \]
\[ = \left( \frac{3}{2} \right)^{- {12}^{}} \]
\[ = \left( \frac{2}{3} \right)^{12}\] →(a−1 = 1/a)
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