What is the value of $(5^{2})^{2} + (2^{2})^{3}$ ?

658

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689

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698

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589

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Solution

The correct option is B 689
By the Laws of Exponents, $(a^{m})^{n} = a^{m n}$ .

So, $(5^{2})^{2} = 5^{4} = 5 \times 5 \times 5 \times 5 = 625$
$(2^{2})^{3} = 2^{6} = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 64$

$\Rightarrow (5^{2})^{2} + (2^{2})^{3} = 625 + 64 = 689$

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