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Negative and Zero Exponents

Q: What is a negative exponent?

A: A number raised to a negative exponent produces the reciprocal of that number. Recall that a reciprocal is just 1 divided by the number. It is very useful to memorize these identities:

a^(-1) = 1/a
a^(- n) = 1/a^n
(a/b)^(- n) = (b/a)^n = b^n/a^n


Q: How do I evaluate a zero exponent?

A: Any number raised to the power of zero is equal to 1.

8^0=1, 15^0=1, 100^0=1, or in general: x^0=1

Why? Because:

x^0 = x^(n-n) = x^n/x^n = 1