Number systems — Maths STD 9 — Question

 We have to find the value of $4^{2 x-2}$ provided $(16)^{2 x+3}=(64)^{x+3}$
So,
$(16)^{2 x+3}=(64)^{x+3}$
$\left(2^4\right)^{2 x+3}=\left(2^6\right)^{x+3}$
$2^{8 x+12}=2^{6 x+18}$
Equating the power of exponents we get
$8x +12 = 6x +18$
$8x - 6x = 18 - 12$
$2x = 6$
$\text{x}=\frac{6}{2}$
$x = 3$
The value of $4^{2 x-2}$ is
$=4^{2 x-2}$
$=4^{2 \times 3-2}$
$=4^{6-2}$
$=4^4$
$=256$
Hence the correct alternative is $b.$