Question

Value of $(256{)}^{0.16}\times (256{)}^{0.09}$ is:

• A. 4
• B. 16
• C. 64
• D. $256.25$

Answer 1

The correct option is A

4

Explanation for the correct option:

Option (a): 4

The given expression is $(256{)}^{0.16}\times (256{)}^{0.09}$.

We need to simplify it.

Simplify it by using the formula of indices $a^b\times a^c=a^{b+c}$.

We obtain,

$=(256{)}^{0.16}\times (256{)}^{0.09}$

$$\begin{gathered} ={\left(256\right)}^{0.16+0.09} \\ ={\left(256\right)}^{0.25} \\ ={\left(256\right)}^{\frac{1}{4}} \\ ={\left(4\right)}^{4\times \frac{1}{4}} \\ =4 \end{gathered}$$

Hence, the correct option is (a). The value of the given expression $(256{)}^{0.16}\times (256{)}^{0.09}$ is 4.