The digit in the unit's place of $6^{500}$ is:

To find the unit's digit of $6^{500}$, examine the pattern in the unit's digits of powers of 6.

Calculate the first few powers of 6:

$6^1 = 6$ (unit's digit: 6)

$6^2 = 36$ (unit's digit: 6)

$6^3 = 216$ (unit's digit: 6)

$6^4 = 1,296$ (unit's digit: 6)

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Every power of 6 ends in 6.

When any number ending in 6 is multiplied by 6, the result always ends in 6.

Example: $6 \times 6 = 36$, then $36 \times 6 = 216$, then $216 \times 6 = 1,296$

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Since every power of 6 has 6 in the unit's place, this holds for any exponent including 500.

Therefore, the unit's digit of $6^{500}$ is $6$.