Question

The number obtained after dividing the number formed by the last three digits of $17^{256}$ by $100$ is

Answer 1

Answer: 6.81

Last three digits of $17^{256}$
$={\left(289\right)}^{128}={\left(-1+290\right)}^{128}$
${=}^{128}{C}_0{\left(-1\right)}^{128}{-}^{128}{C}_1\cdot 290{+}^{128}{C}_2\cdot {\left(290\right)}^2+.......$
$=1-128\times 290+64\times 127\times 29^2\times 100+.......$
$=1-......120+.....800+.......$
$=681$
Hence, $\frac{681}{100}=6.81$