Question

The value of (256)^0.16 × (256)^0.09 is ________.

Answer 1

$$\begin{gathered} {\left(256\right)}^{0.16}\times {\left(256\right)}^{0.09}={\left(256\right)}^{0.16+0.09} \\ ={\left(256\right)}^{0.25} \\ ={\left(256\right)}^{\frac{25}{100}} \\ ={\left(256\right)}^{\frac{1}{4}} \\ ={\left(2^8\right)}^{\frac{1}{4}} \\ ={\left(2\right)}^{8\times \frac{1}{4}} \\ ={\left(2\right)}^2 \\ =4 \end{gathered}$$

Hence, the value of (256)^0.16 × (256)^0.09 is 4.