To get from 5^0 to 5^-3, we need to apply two mathematical concepts: the first is the rule that any number raised to the power of 0 is equal to 1, and the second is the concept of negative exponents.
First, we know that 5^0 = 1, since any number raised to the power of 0 is equal to 1.
To get to 5^-3, we use the concept of negative exponents, which tells us that a number raised to a negative exponent is equal to 1 divided by the number raised to the corresponding positive exponent. In other words:
a^(-n) = 1 / a^n
Using this formula, we can rewrite 5^-3 as 1/5^3. Substituting 5^0 with 1, we get:
5^0 = 1
1 / 5^3 = 1 / (5 x 5 x 5) = 1/125
Therefore, 5^0 = 1 and 5^-3 = 1/125.