Find the value of the expression: ${(3^{2})}^{2} - {({(- 2)}^{3})}^{2} - {(- (5^{2}))}^{2}$

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Solution

The given expression ${(3^{2})}^{2} - {({(- 2)}^{3})}^{2} - {({- (5)}^{2})}^{2}$ can be simplified as follows:
${(3^{2})}^{2} - {({(- 2)}^{3})}^{2} - {({- (5)}^{2})}^{2} = 3^{2 \times 2} - {(- 2)}^{3 \times 2} - (- (5)^{2 \times 2}) (∵ {(x^{m})}^{n} = x^{m \times n}) = 3^{4} - {(- 2)}^{6} - (- (5)^{4})$
$= 81 - 64 (- 625) = 81 - 64 + 625 = 706 - 64 = 642$
Hence, ${(3^{2})}^{2} - {({(- 2)}^{3})}^{2} - {({- (5)}^{2})}^{2} = 642$

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