The value of

Question:

The value of $(256)^{0.16} \times(256)^{0.09}$ is

(a) 4

(b) 16

(c) 64

(d) $256.25$

Solution:

(a)

(a) $(256)^{0.16} \times(256)^{0.09}=(256)^{\frac{16}{100}} \times(256)^{\frac{9}{100}}$

$=(256)^{\frac{16}{100}}+\frac{9}{100}$        $\left[\because x^{a} \cdot x^{b}=x^{a+b}\right]$

$=(256)^{\frac{25}{100}}=(256)^{\frac{1}{4}}$ 

$=\left(4^{4}\right)^{\frac{1}{4}}=4$           $\left[\because\left(a^{m}\right)^{n}=a^{m n}\right]$

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