Q.3 Express each of the following numbers using exponential notation:
(i) 512
(ii) 343
(iii) 729
(iv) 3125


Answer :

(i) $$ \begin{array}{|l} \llap{2~~~~} 512 \\ \hline \llap{2~~~~} 216 \\ \hline \llap{2~~~~} 128 \\ \hline \llap{2~~~~} 64 \\ \hline \llap{2~~~~} 32 \\ \hline \llap{2~~~~} 16 \\ \hline \llap{2~~~~} 8 \\ \hline \llap{2~~~~} 4 \\ \hline \llap{2~~~~} 2 \\ \hline \llap{~~~~} 1 \\ \hline \end{array} $$ 512= 2×2×2×2×2×2×2×2×2 = \(2^9\)
(ii) $$ \begin{array}{|l} \llap{7~~~~} 343 \\ \hline \llap{7~~~~} 49 \\ \hline \llap{7~~~~} 7 \\ \hline \llap{~~~~} 1 \\ \hline \end{array} $$ 343 = 7×7×7 = \(7^3\)
(iii) $$ \begin{array}{|l} \llap{3~~~~} 729 \\ \hline \llap{3~~~~} 243 \\ \hline \llap{3~~~~} 81 \\ \hline \llap{3~~~~} 27 \\ \hline \llap{3~~~~} 9 \\ \hline \llap{~~~~} 3 \\ \hline \end{array} $$ 729 = 3×3×3×3×3×3 = \(3^6\)
(iv) $$ \begin{array}{|l} \llap{5~~~~} 3125 \\ \hline \llap{5~~~~} 625 \\ \hline \llap{5~~~~} 125 \\ \hline \llap{5~~~~} 25 \\ \hline \llap{5~~~~} 5 \\ \hline \llap{~~~~} 1 \\ \hline \end{array} $$ 3125 = 5×5×5×5×5= \(5^5 \)

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