Question

find n if (2²^n)⁴÷(2³^n)²=2⁴^n-¹​

Answer 1

Answer:

$I \: \: referred \: \: these \: \: formulas \: : \\ {( {a}^{m} )}^{n} = {a}^{m \times n} \\ \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} \\ if \: \: {a}^{m} = {a}^{n}, \: \: then \: \: m = n$

Step-by-step explanation:

$\frac{ { { ({2}^{2} }^{n}) }^{4} }{ { { ({2}^{3} }^{n}) }^{2} } = {( {2}^{4} )}^{n - 1} \\ \frac{ { {2}^{(2 \times n \times 4)}} }{ {2}^{( 3\times n \times 2)} } = {2}^{4 \times (n - 1)} \\ \frac{ {2}^{8n} }{ {2}^{6n} } = {2}^{4n - 4} \\ {2}^{8n - 6n} = {2}^{4n - 4} \\ {2}^{2n} = {2}^{4n - 4} \\ 2n = 4n - 4 \\ 4 = 4n - 2n \\ 4 = 2n \\ \frac{4}{2} = n \\ \frac{ _{2} \: \cancel 4}{ _{1} \: \cancel 2} = n \\ \boxed{ \underline{ \underline{ 2 }}= n}$