a)

$4^{-2}={\left(\frac{1}{4}\right)}^2=\frac{1}{4^2}=\frac{1}{16}$  

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b)

$5^{-4}={\left(\frac{1}{5}\right)}^4=\frac{1}{5^4}=\frac{1}{625}$  

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c)

$6^{-3}={\left(\frac{1}{6}\right)}^3=\frac{1}{6^3}=\frac{1}{216}$  

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d)

$9^{-3}={\left(\frac{1}{9}\right)}^3=\frac{1}{9^3}=\frac{1}{729}$  

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e)

${\left(-4\right)}^{-1}={\left(-\frac{1}{4}\right)}^1=-\frac{1}{4}$

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f)

${\left(-5\right)}^{-2}={\left(-\frac{1}{5}\right)}^2=\frac{1}{{\left(-5\right)}^2}=\frac{1}{25}$   

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g)

${\left(-2\right)}^{-4}={\left(-\frac{1}{2}\right)}^4=\frac{1}{{\left(-2\right)}^4}=\frac{1}{16}$  

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h)

${\left(-3\right)}^{-5}={\left(-\frac{1}{3}\right)}^5=\frac{1}{{\left(-3\right)}^5}=-\frac{1}{243}$