waecmaths question:
If ${{2}^{n}}=128$ , find the value of $({{2}^{n-1}})({{5}^{n-2}})$
Option A:
$5{{(10)}^{6}}$
Option B:
$2({{10}^{6}})$
Option C:
$5({{10}^{5}})$
Option D:
$2({{10}^{5}})$
waecmaths solution:
$\begin{align} & {{2}^{n}}=128 \\ & {{2}^{n}}={{2}^{7}} \\ & n=7 \\ & ({{2}^{n-1}})({{5}^{n-2}})=({{2}^{7-1}})({{5}^{7-2}})={{2}^{6}}\times {{5}^{5}} \\ & ({{2}^{n-1}})({{5}^{n-2}})=2({{2}^{5}}\times {{5}^{5}})=2{{(2\times 5)}^{5}}=2({{10}^{5}}) \\\end{align}$
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