Question

if \[x = \left( \frac{3}{2} \right)^2 \times \left( \frac{2}{3} \right)^{- 4}\], find the value of x⁻².

Answer 1

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)