Question

Express 3600 as a product of powers of its prime factors.

Answer 1

Performing the prime factorisation of 3600:

$$\begin{array}{cc}2& 3600\\ 2& 1800\\ 2& 900\\ 2& 450\\ 3& 225\\ 3& 75\\ 5& 25\\ 5& 5\\ & 1\end{array}$$

So,

3,600 = $2\times 2\times 2\times 2\times 3\times 3\times 5\times 5$

$\therefore$ $3,600=2^4\times 3^2\times 5^2$