Answer:
It should be [tex]\sqrt{\frac{1}{216} }[/tex] or [tex]\frac{1}{6\sqrt{6} }[/tex] (they're both the same thing, one is just more simplified than the other) unless I misread the question somehow.
Step-by-step explanation:
Simplify
[tex](\sqrt{10^2-4^3} )^{\frac{-3}{2} }[/tex]
[tex]\sqrt{100-64} ^{\frac{-3}{2} }[/tex]
[tex]\sqrt{36} ^\frac{-3}{2}[/tex]
[tex](6)^\frac{-3}{2}[/tex]
Now, using the fractional exponent rule, we know this is the same as:
[tex]\sqrt{6^{-3} }[/tex]
[tex]\sqrt{\frac{1}{216} }[/tex]
