Mark the correct alternative in the following question:

${\{{(33)}^{2} - {(31)}^{2}\}}^{\frac{5}{7}} = (a) 64 (b) 16 (c) 32 (d) 4$

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Solution

Since,

${\{{(33)}^{2} - {(31)}^{2}\}}^{\frac{5}{7}} = {\{1089 - 961\}}^{\frac{5}{7}} = {\{128\}}^{\frac{5}{7}} = {\{2^{7}\}}^{\frac{5}{7}} = 2^{7 \times \frac{5}{7}} [As, {(x^{m})}^{n} = x^{m n}] = 2^{5} = 32$

Hence, the correct alternative is option (c).

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