Question

Evaluate:
(i) 4⁻³
(ii) ${\left(\frac{1}{2}\right)}^{-5}$
(iii) ${\left(\frac{4}{3}\right)}^{-3}$
(iv) ${\left(-3\right)}^{-4}$
(v) ${\left(\frac{-2}{3}\right)}^{-5}$

Answer 1

(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) ${\left(-3\right)}^{-4}={\left(\frac{-1}{3}\right)}^4=\frac{(-1{)}^4}{3^4}=\frac{1}{81}$

(v) ${\left(\frac{-2}{3}\right)}^{-5}={\left(\frac{-3}{2}\right)}^5=\frac{{\left(-3\right)}^5}{2^5}=\frac{-243}{32}$