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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) $(2^{2}+3^{2}-4^{2}) \div(\frac{3}{2})^{2}=(4+9-16) \div \frac{9}{4}$
$=-3 \times \frac{4}{9}$
$=\frac{-1 \times 4}{3}$
$=\frac{-4}{3}$
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