Which is larger: ${(100)}^{4}$ or ${(125)}^{3}$ ?

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Solution

${(100)}^{4} = (2 \times 2 \times 5 \times 5)^{4} = 2^{4} \times 2^{4} \times 5^{4} \times 5^{4} = 16 \times 16 \times 25 \times 25 = 100000000$
${(125)}^{3} = (5 \times 5 \times 5) = 5^{3} \times 5^{3} \times 5^{3} = 1953125$
So, $100000000 > 1953125$
Thus, ${(100)}^{4} > {(125)}^{3}$

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