Express each of following as a product of powers of their prime factors: $9000$

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Solution

Using prime factorization of $9000$ , we have,
$\begin{matrix} 2 & 9000 2 & 4500 2 & 2250 3 & 1125 3 & 375 5 & 125 5 & 25 5 & 5 1 \end{matrix}$
$\Rightarrow 9000 = 2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 5 \times 5$
$∴ 9000 = 2^{3} \times 3^{2} \times 5^{3}$

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