Question

(b) 2^(4n) x 2^(2n) = 256​

Answer 1

n = 4/3

Step-by-step explanation:

How to solve ?

1) This question is basically related to Laws of indices. So, Law of Indices will be use.

2) Break the exponent in smallest form as, 8 =2³

or 27 = 3³ so on...

3) Simplify till answer.

Solution:

${2}^{(4n)} \times {2}^{(2n)} = 256 \\ \\ {2}^{(4n + 2n)} = {2}^{8} [\because \: {2}^{8} = 256] \\ \\ {6n} = 8 \\ \\ n = \frac{8}{6} = \frac{4}{3}$

Law of Indices

${a}^{b} \times {a}^{c} = {a}^{(b + c)} \\ \\ \frac{ {a}^{n} }{ {a}^{m} } = {a}^{(n - m)} \\ \\ { ({a}^{b}) }^{c} = {a}^{ bc } \\ \\ {a}^{ - 1} = \frac{1}{a}$