Express each of the following as product of powers of their prime factors:
$(i)$ $648$ $(i i)$ $405$
$(i i i)$ $540$ $(i v)$ $3, 600$

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Solution

(i) $648 = 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3 = 2^{3} \times 3^{4}$
$\begin{matrix} 2 & 648 2 & 324 2 & 162 3 & 81 3 & 27 3 & 9 3 & 3 1 \end{matrix}$
(ii) $405 = 3 \times 3 \times 3 \times 3 \times 5 = 3^{4} \times 5$
$\begin{matrix} 3 & 405 3 & 135 3 & 45 3 & 15 5 & 5 1 \end{matrix}$
(iii) $540 = 2 \times 2 \times 3 \times 3 \times 3 \times 5 = 2^{2} \times 3^{3} \times 5$
$\begin{matrix} 2 & 540 2 & 270 3 & 135 3 & 45 3 & 15 5 & 5 1 \end{matrix}$
(iv) $3600 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 5 = 2^{4} \times 3^{2} \times 5^{2}$
$\begin{matrix} 2 & 3600 2 & 1800 2 & 900 2 & 450 3 & 225 3 & 75 5 & 25 5 & 5 1 \end{matrix}$

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648

Question 5(iv)
Express each of the following as the product of powers of their prime factors:
(iv) 3,600

Question 5(ii)
Express each of the following as product of powers of their prime factors:
(ii) 405

Question 5(iii)
Express each of the following as product of powers of their prime factors:
(iii) 540

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