Question

Determine the digit in the unit position 1^21*17^17*21^21

Answer 1

Just see my friend,
1^21=1,
1 * 17=1
Then
1^17=1
1*21=1
1^21=1

Answer 2

Given:

$1^{21}*17^{17}*21^{21}$

To Find:

The value at the unit place of the above expression.

Solution:

Let $x_1=1^{17}$,  $x_2=17^{17}$ and $x_3=21^{21}$

Let us consider $x_1$:

Unit place of $1^{21}$ will be 1 because we know that 1 raised to any exponent is 1 only.

Now let us consider $x_2$:

Since, the unit place of 17 is 7, the unit place of $17^{17}$ will be equal to that of the unit place of $7^{17}$

Also $7^{17}=7^4*7^4*7^4*7^4*7^1$

             $=(2401)^4*7$

Therefore the unit place of $x_2$ will be 7.

Finally considering $x_3$:

Since, the unit place of 21 is 1, the unit place of $21^{21}$ will also have 1 at its unit place.

So, the unit place of $x_1 *x_2*x_3$ will be 7.

Hence, the unit place of the given expression will be 7.