To simplify the expression $5^0 \cdot 2^{-3}$:

1. Any number raised to the power of 0 is 1, so: $5^0 = 1$

2. The term $2^{-3}$ can be rewritten using the negative exponent rule: $2^{-3} = \frac{1}{2^3}$

   Simplifying further: $2^3 = 2 \cdot 2 \cdot 2 = 8, \quad \text{so } 2^{-3} = \frac{1}{8}$

3. Now, multiply the results: $1 \cdot \frac{1}{8} = \frac{1}{8}$

Thus, the final result is: $\frac{1}{8}$

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Do you have any questions or would you like further details?

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Related Questions:

1. What happens when you multiply numbers with the same base but different exponents?
2. How do you simplify expressions involving fractional exponents?
3. Can you explain the zero exponent rule with examples?
4. How is $a^{-n}$ defined, and why does it result in a reciprocal?
5. What are the properties of exponents used in more complex equations?

Tip: Always remember to evaluate powers of zero and negative exponents separately before combining them!