Question:
Evaluate:
(i) $4^{-3}$
(ii) $\left(\frac{1}{2}\right)^{-5}$
(iii) $\left(\frac{4}{3}\right)^{-3}$
(iv) $(-3)^{-4}$
(v) $\left(\frac{-2}{3}\right)^{-5}$
Solution:
(i) $4^{-3}=\frac{1}{4^{3}}=\frac{1}{64}$
(ii) $\left(\frac{1}{2}\right)^{-5}=2^{5}=32$
(iii) $\left(\frac{4}{3}\right)^{-3}=\left(\frac{3}{4}\right)^{3}=\frac{3^{3}}{4^{3}}=\frac{27}{64}$
(iv) $(-3)^{-4}=\left(\frac{-1}{3}\right)^{4}=\frac{(-1)^{4}}{3^{4}}=\frac{1}{81}$
(v) $\left(\frac{-2}{3}\right)^{-5}=\left(\frac{-3}{2}\right)^{5}=\frac{(-3)^{5}}{2^{5}}=\frac{-243}{32}$
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