Simplify:
(i) $ \left(3^{2}+2^{2}\right) \times\left(\frac{1}{2}\right)^{3} $
(ii) $ \left(3^{2}-2^{2}\right) \times\left(\frac{2}{3}\right)^{-3} $
(iii) $ \left[\left(\frac{1}{3}\right)^{-3}-\left(\frac{1}{2}\right)^{-3}\right] \div\left(\frac{1}{4}\right)^{-3} $
(iv) $ \left(2^{2}+3^{2}-4^{2}\right) \div\left(\frac{3}{2}\right)^{2} $

To do:  

We have to simplify the given expressions.

Solution:

(i) $(3^{2}+2^{2}) \times(\frac{1}{2})^{3}=(9+4) \times \frac{1}{8}$

$=13 \times \frac{1}{8}$

$=\frac{13}{8}$

(ii) $(3^{2}-2^{2}) \times(\frac{2}{3})^{-3}=(9-4) \times(\frac{3}{2})^{3}$

$=5 \times \frac{27}{8}$

$=\frac{135}{8}$

(iii) $[(\frac{1}{3})^{-3}-(\frac{1}{2})^{-3}] \div(\frac{1}{4})^{-3}=[(3)^{3}-(2)^{3}] \div(4)^{3}$

$=(27-8) \div 64$

$=19 \div 64$

$=\frac{19}{64}$

(iv) $(2^{2}+3^{2}-4^{2}) \div(\frac{3}{2})^{2}=(4+9-16) \div \frac{9}{4}$

$=-3 \times \frac{4}{9}$

$=\frac{-1 \times 4}{3}$

$=\frac{-4}{3}$