Express the following in exponential form :
${(1.8)}^{7}$

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Solution

$(1.8)^{7}$
$(1 + (0.8)^{7}$
$[1 +^{7} C_{1} (0.8) +^{7} C_{2} C_{2} (0.8)^{2} +^{7} C_{3} (0.8)^{3} +^{7} C_{4} (0.8)^{4} +^{7} C_{5} (0.8)^{5} +^{7} C_{6} (0.8)^{6} +^{7} C_{7} (0.8)^{7}]$
$\Rightarrow [1 + 7 (0.8) + 21 (0.8)^{2} + 35 (0.8)^{3} + 35 (0.8)^{4} + 21 (0.8)^{5} + 7 (0.8)^{6} + (0.8)]$
$(0.8)^{7} = (1 + (0.8)^{7} + 21 ((0.8)^{2} + (0.8)^{6}) + 7 ((0.8) + (0.8)^{6}) + 35 ((0.8)^{4} + (0.8)^{5}))$

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