Question:
The value of $(256)^{0.16} \times(256)^{0.09}$ is
(a) 4
(b) 16
(c) 64
(d) $256.25$
Solution:
(a)
(a) $(256)^{0.16} \times(256)^{0.09}=(256)^{\frac{16}{100}} \times(256)^{\frac{9}{100}}$
$=(256)^{\frac{16}{100}}+\frac{9}{100}$ $\left[\because x^{a} \cdot x^{b}=x^{a+b}\right]$
$=(256)^{\frac{25}{100}}=(256)^{\frac{1}{4}}$
$=\left(4^{4}\right)^{\frac{1}{4}}=4$ $\left[\because\left(a^{m}\right)^{n}=a^{m n}\right]$