Q:  What is a negative exponent?  What does a negative exponent do?

A:  A negative exponent is just notation that can be used to represent a reciprocal.  Let me show you some examples:

x ^{– 1} = 1/x¹ or 1/x

x^-2 = 1/x²

4 ^{– 1} = 1/4¹ or 1/4

4 ^{– 2} = 1/4² = 1/16

Those are the basics.  Let’s look at a few more complicated examples of how negative exponents affect an expression:

3x ^{– 4} = 3/x⁴

4x⁶y ^{– 3} = 4x⁶/y³

OR… If the negative exponent is affecting something in a denominator, it will move it to the numerator like so:

1/x ^{– 5} = 1*x⁵ = x⁵

6/y ^{– 7} = 6y⁷

These are just a few basic examples to show you how negative exponents work. Of course things can get more difficult.