Question

if 2-ⁿx8²ⁿ+¹x16²ⁿ/4³ⁿ= 1/16, find the value of .

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Answer 1

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Answer 2

$\\ = > \: \: \: \: \: \frac{ {2}^{ - n} \times {8}^{2n + 1} \times {16}^{2n} }{ {4}^{3n} } = \frac{1}{16} \\ \\ = > \frac{ {2}^{ - n} \times {2}^{3(2n + 1)} \times {2}^{4(2n)} }{ {2}^{2(3n)} } = \frac{1}{ 16 } \\ \\ = > \: \: \: \: \: \: \: \frac{ {2}^{ - n} \times {2}^{6n + 3} \times {2}^{8n} }{ {2}^{6n} } = \frac{1}{ {2}^{4} } </p><p>$

$\\ = > \: \frac{ {2}^{ - n + 6n + 3 + 8n} }{ {2}^{6n} } = \frac{1}{ {2}^{4} } \\ \\ = > \: \: \: \: \: \: \: \: \: \: \: \frac{ {2}^{13n + 3} }{2 {}^{6n} } = {2}^{ - 4} \\ \\ = > \: \: \: \: \: \: {2}^{13n + 3 - 6n} = {2}^{ - 4}$

$\\ = > \: \: \: \: \: \: \: \: \: \: \: \: {2}^{7n + 3} = {2}^{ - 4} \\ \\ (2) = eliminated \\ \\ = > \: \: \: \: \: \: \: \: \: \: 7n + 3 = - 4 \\ = > \: \: \: \: \: \: \: \: \: \: 7n = - 4 - 3 \\ = > \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 7n = - 7$

$= > \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: n = \frac{ - 7}{7} \\ \\ = > \: \: \huge \: n = - 1$

so, your required answer to this question is

—1

i.e →

n = —1

Step-by-step explanation:

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