The given expression is an application of an exponential equation. The result shows that [tex]3^{2x} = \frac{1}{4}[/tex] if [tex]3^{-x}=2[/tex]
Given that [tex]3^{-x}=2[/tex]
This can also be expressed as [tex]\frac{1}{3^x} =2\\[/tex]
Cross multiply
[tex]\frac{1}{3^x} =2\\3^x = \frac{1}{2}[/tex]
Take the square root of both sides
[tex](3^x)^2 = (\frac{1}{2} )^2\\3^{2x} = \frac{1}{4}[/tex]
The result shows that [tex]3^{2x} = \frac{1}{4}[/tex] if [tex]3^{-x}=2[/tex]
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