Zero and negative indices

p² ÷ p²

We need to look at this in two ways.

Using the rule for dividing indices:

p² ÷ p² = p^2-2

= p⁰

But we know that anything divided by itself is 1.

So p⁰ = 1.

Anything to the power of 0 is equal to 1.

3² ÷ 3⁴

Using the rule for dividing indices:

3² ÷ 3⁴ = 3^-2

But we also know that:

So 3^-2 = \(\frac{1}{3^2}\)

which is equal to \(\frac{1}{9}\) when evaluated.

For negative indices, a^-m = \(\frac{1}{a^m}\)

Question

What is the value of 2^-3 ?