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# Q.5 Express each of the following as the product of powers of their prime (i) 648 (ii) 405 (iii) 540 (iv) 3600

(i) $$\begin{array}{|l} \llap{2~~~~} 648 \\ \hline \llap{2~~~~} 324 \\ \hline \llap{2~~~~} 162 \\ \hline \llap{3~~~~} 81 \\ \hline \llap{3~~~~} 27 \\ \hline \llap{3~~~~} 9 \\ \hline \llap{3~~~~} 3 \\ \hline 1 \end{array}$$ 648= $$2^3× 3^4$$
(ii) $$\begin{array}{|l} \llap{3~~~~} 405 \\ \hline \llap{3~~~~} 135 \\ \hline \llap{3~~~~} 45 \\ \hline \llap{3~~~~} 15 \\ \hline \llap{5~~~~} 5 \\ \hline \llap{~~~~} 1 \\ \hline \end{array}$$ 405= $$3^4×5^1$$
(iii) $$\begin{array}{|l} \llap{2~~~~} 540 \\ \hline \llap{2~~~~} 270 \\ \hline \llap{3~~~~} 135 \\ \hline \llap{3~~~~} 45 \\ \hline \llap{3~~~~} 15 \\ \hline \llap{5~~~~} 5 \\ \hline \llap{~~~~} 1 \\ \hline \end{array}$$ $$540 = 2^2×3^3×5^1$$
(iv) $$\begin{array}{|l} \llap{2~~~~} 3600 \\ \hline \llap{2~~~~} 1800 \\ \hline \llap{2~~~~} 900 \\ \hline \llap{2~~~~} 450 \\ \hline \llap{3~~~~} 225 \\ \hline \llap{3~~~~} 75 \\ \hline \llap{5~~~~} 25 \\ \hline \llap{5~~~~} 5 \\ \hline 1 \end{array}$$ $$3600 = 2^4×3^2×5^2$$