16X2n+1-4X2n /16X2n+2-2X2n+2 I need to simplify and find the value of n - Maths - Exponents and Powers

Question

16X2n+1-4X2n
/16X2n+2-2X2n+2
I need to simplify and find the value of n

Shridhar Kaushik · Accepted Answer

We have,

$\frac{16 \times 2^{n + 1} - 4 \times 2^{n}}{16 \times 2^{n + 2} - 2 \times 2^{n + 2}} = \frac{2^{n} [16 \times 2 - 4 \times 1]}{2^{n + 2} [16 - 2]} = \frac{32 - 4}{14 \times 2^{n + 2 - n}} [∵ a^{n} = \frac{1}{a^{- n}}] = \frac{28}{14 \times 4} = \frac{1}{2}$

Thus, the value of given expression is $\frac{1}{2}$ for any value of n.