Evaluate:

Question:

Evaluate:

(i) 5−2

(ii) (−3)−2

(iii) $\left(\frac{1}{3}\right)^{-4}$

(iv) $\left(\frac{-1}{2}\right)^{-1}$

 

Solution:

(i) $5^{-2}=\frac{1}{5^{2}} \quad \quad \cdots\left(a^{-n}=1 /\left(a^{n}\right)\right)$

$=\frac{1}{25}$

$(\mathrm{ii})(-3)^{2}=\frac{1}{3^{2}} \quad \ldots\left(a^{-n}=1 /\left(a^{n}\right)\right)$

$=\frac{1}{9}$

(iii) $\left(\frac{1}{3}\right)^{-4}=\frac{1}{(1 / 3)^{4}} \quad \cdots\left(a^{-n}=1 /\left(a^{n}\right)\right)$

$=\frac{1}{1 / 81}$

= 81

$($ iv $)\left(\frac{-1}{2}\right)^{-1}=\left(\frac{1}{-1 / 2}\right) \quad \cdots\left(a^{-1}=1 /(a)\right)$

$=-2$

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