Answer:
1
Step-by-step explanation:
Given the expression [tex]\left[\left(\frac{2}{5}\right)^{12} \left(\frac{3}{16}\right)^{-8}\right] \cdot \left[\left(\frac{2}{5}\right)^{12} \left(\frac{3}{16}\right)^{-8}\right]^{-1}[/tex]
According to indices:
[tex]a^{-1} = \frac{1}{a}[/tex]
Applying this to the question:
[tex]\left[\left(\frac{2}{5}\right)^{12} \left(\frac{3}{16}\right)^{-8}\right]^{-1} = \frac{1}\left\left(\frac{2}{5}\right)^{12} \left(\frac{3}{16}\right)^{-8}\right}[/tex]
Hence:
[tex]\left[\left(\frac{2}{5}\right)^{12} \left(\frac{3}{16}\right)^{-8}\right] \cdot \left[\left(\frac{2}{5}\right)^{12} \left(\frac{3}{16}\right)^{-8}\right]^{-1} = \frac{\left[\left(\frac{2}{5}\right)^{12} \left(\frac{3}{16}\right)^{-8}\right]}{\left[\left(\frac{2}{5}\right)^{12} \left(\frac{3}{16}\right)^{-8}\right]} \\\\\left[\left(\frac{2}{5}\right)^{12} \left(\frac{3}{16}\right)^{-8}\right] \cdot \left[\left(\frac{2}{5}\right)^{12} \left(\frac{3}{16}\right)^{-8}\right]^{-1} = 1[/tex]
Hence the right answer is 1
