Question

find the value of 'n' such that 2^ 2n+1 ×4 ^3 = 2 ^8 by giving suitable reason.​

Answer 1

I think the expression is 2^(2n+1)*4^3=2^8
2^(2n+1)*4^3=2^8
=>2^(2n+1)*2^6=2^8
=>2^(2n+1)=2^2
By equating the powers we get,
2n+1=2
=>2n=1
=>n=1/2

Answer 2

$\large \underline \text{Question: - }$

• Find the value of 'n' such that 2^(2n+1) × 4³ = 2⁸ by giving suitable reason.

$\large \underline \text{Solution: - }$

Given that,

• ${2}^{2n + 1} \times {4}^{3} = {2}^{8}$

Finding the value of 'n',

$\implies {2}^{2n + 1} \times {4}^{3} = {2}^{8} \\ \\ \implies {2}^{2n + 1} \times {( {2}^{2} )}^{3} = {2}^{8} \: \: \: \: \: [ {( {x}^{a} )}^{b} = {x}^{a \times b} ] \\ \\ \implies {2}^{2n + 1} \times {2}^{2 \times 3} = {2}^{8} \\ \\ \implies {2}^{2n + 1} \times {2}^{6} = {2}^{8} \: \: \: \: \: [ {x}^{a} \times {x}^{b} = {x}^{a + b} ] \\ \\ \implies {2}^{(2n + 1) + 6} = {2}^{8} \\ \\ \implies {2}^{2n + 7} = {2}^{8}$

Comparing both sides,

$\implies 2n + 7 = 8 \\ \\ \implies 2n = 8 - 7 \\ \\ \implies 2n = 1 \\ \\ \implies \boxed{n = \frac{1}{2} }$

Therefore,

• The value of 'n' is 1/2.

$\\ \large \underline \text{Required Answer: - }$

• The value of 'n' is 1/2.