Question

2power-n.8power2n+1.16power 2n/4power 3n

Answer 1

Given:

2power-n.8power2n+1.16power 2n/4power 3n

To find:

To find the value of

2power-n.8power2n+1.16power 2n/4power 3n

Solution:

From given, we have,

2 power -n. 8 power 2n+1. 16 power 2n/ 4 power 3n

Now consider,

4power 3n = 2 power 6n

8power2n+1 = 2 power 3(2n + 1)

16 power 2n = 2 power 8n

so, we have,

2 power -n. 8 power 2n+1. 16 power 2n/ 4 power 3n

= 2 power -n.  2 power 3(2n + 1). 2 power 8n/ 2 power 6n

further solving, we get,

= 2 power {-n + 3 (2n + 1) + 8n} / 2 power 6n

= 2 power 7n + 3.

$\dfrac{2^{-n}\cdot \:8^{2n+1}\cdot \:16^{2n}}{4^{3n}}\\\\=\dfrac{2^{3\left(2n+1\right)}\cdot \:2^{-n}\cdot \:2^{8n}}{2^{6n}}\\\\=\dfrac{2^{-n+3\left(2n+1\right)+8n}}{2^{6n}}\\\\=2^{7n+3}$

Answer 2

Step-by-step explanation:

Given 2power-n.8power2n+1.16power 2n/4power 3n

• Given we need to solve using law of exponents.
• So we have
• 2^-n x 8^2n + 1 x 16^ 2n / 4^3n
• We can write this as
• 2^-n x (2^3)^2n + 1 x (2^4)^2n / (2^2)^3n
• 2^-n x 2^6n + 3 x 2^ 8n / 2^6n
• By using the law a^m x a^n = a^m + n we get
• 2^-n x 2^6n + 3 x 2^8n / 2^6n
• 2^-n + 6n + 3 + 8n / 2^6n
• 2^13n + 3 / 2^6n
• By using a^m / a^n = a^m – n we get
• 2^13n + 3 – 6n
• = 2^7n + 3

Reference link will be

https://brainly.in/question/2870399