Question 21

Which of the following is not true?
(a) $3^{2} > 2^{3}$
(b) $4^{3} = 2^{6}$
(c) $3^{3} = 9$
(d) $2^{5} > 5^{2}$

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Solution

For option (a), $3^{2} > 2^{3} 3 \times 3 > 2 \times 2 \times 2 9 > 8 (true)$

For option (b), $4^{3} = 2^{6} (2^{2})^{3} = 2^{6} 2^{6} = 2^{6} (true)$

For option (c), $3^{3} = 9 3 \times 3 \times 3 = 9 27 \neq 9 (not true)$

For option (d), $2^{5} > 5^{2} 2 \times 2 \times 2 \times 2 \times 2 > 5 \times 5 32 > 25 (true)$

Hence, option (c) is not true.

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\frac{(3 \frac{2}{3})^{2} - (2 \frac{1}{2})^{2}}{(4 \frac{3}{2})^{2} - (3 \frac{1}{3})^{2}}

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Question 180(vi)

Simplify :
$\frac{(3^{- 2})^{2} \times (5^{2})^{- 3} \times (t^{- 3})^{2}}{(3^{- 2})^{5} \times (5^{3})^{(- 2)} \times (t^{- 4})^{3}}$

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