Question

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

Answer 1

Using prime factorization of $9000$, we have,

$\begin{array}{cc}2& 9000\\ 2& 4500\\ 2& 2250\\ 3& 1125\\ 3& 375\\ 5& 125\\ 5& 25\\ 5& 5\\ & 1\end{array}$
$\Rightarrow 9000=2\times 2\times 2\times 3\times 3\times 5\times 5\times 5$

$\therefore 9000=2^3\times 3^2\times 5^3$