Look for patterns.
264 raised to the 1st power = 264...the unit's digit is the right most digit which is 4.
264 raised to the 2nd power is 69696....the unit's digit is 6.
264 raised to the 3rd power ...unit's digit is 4.
264 raised to the 4th power ...unit's digit is 6.
Whenever the power is odd the unit's digit is 4. Whenever the power is even the unit's digit is 6.
264^102 will have a 6 in the unit's digit. 264^103 will have a 4 in the unit's digit. 6+4 = 10. When those numbers are added the unit's digit will be 0.
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