Exponents Of Real Numbers — Maths STD 9 — Question

We have to find the value of $(256)^{0.16} \times(256)^{0.09}$. So,
By using law of rational exponents
$a^m \times a^n=a^{m+n} \text { we get }$
$(265)^{0.16} \times(256)^{0.09}=(256)^{0.16} \times(256)^{0.09}$
$=(256)^{0.16+0.09}$
$=256^{0.25}$
$=256^{\frac{25}{100}}$
$(256)^{0.16} \times(256)^{0.09}=2^{8 \times \frac{25}{100}}$
$=2^{8 \times \frac{25}{100}}$
$=2^{8 \times \frac{1}{4}}$
$=2^{8 \times \frac{1}{4}}=4$
The value of $(256)^{0.16} \times(256)^{0.09}$ is $4$
Hence the correct choice is $a$.