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1. Start by applying the rule of exponents that states when dividing numbers with the same base, you subtract the exponents.
2. In this case, the expression 19^8 / 19^5 can be simplified to 19^(8-5).
3. Subtract the exponents: 8 - 5 = 3.
4. Therefore, the expression simplifies to 19^3.
5. Calculate 19^3 by multiplying 19 by itself 3 times: 19 * 19 * 19 = 6,859.
6. Therefore, 19^8 / 19^5 is equal to 6,859.