Question

Express as a power of rational number with negative exponent.
(i) ${\left[{\left(\frac{-3}{2}\right)}^{-2}\right]}^{-3}$
(ii) $(2^5÷2^8)\times 2^{-7}$
(ii) $\left[{\left(\frac{2}{3}\right)}^{-3}\times {\left(\frac{4}{9}\right)}^{-1}\right]÷{\left(\frac{2}{3}\right)}^{-4}$

Answer 1

(i) ${\left({\left(\frac{-3}{2}\right)}^{-2}\right)}^{-3}={\left(\frac{-3}{2}\right)}^6={\left(\frac{-2}{3}\right)}^{-6}$

(ii) $(2^5÷2^8){\times }^{-7}$

$\Rightarrow 2^{-3}\times 2^{-7}=2^{-10}$

(iii) $[{\left(\frac{2}{3}\right)}^{-3}\times {\left(\frac{4}{9}\right)}^{-1}]÷{\left(\frac{2}{3}\right)}^{-4}$

$\Rightarrow [{\left(\frac{2}{3}\right)}^{-3}\times {\left(\frac{2}{3}\right)}^{-2}]÷{\left(\frac{2}{3}\right)}^{-4}$

$\Rightarrow {\left(\frac{2}{3}\right)}^{-5}÷{\left(\frac{2}{3}\right)}^{-4}={\left(\frac{2}{3}\right)}^{-1}$