If you've entered the world of exponents, you may already know that a positive exponent has a base – the number at the bottom – and a smaller number on top, which represents the exponent. So for the number yx, y is the base and x is the exponent. The number value of x can be either positive or negative, which tells you whether the exponent represents multiplication or division.
TL;DR (Too Long; Didn't Read)
To calculate a negative exponent, write it as a fraction with 1 in the numerator and the positive exponent in the denominator. For example, x-15 would be 1/x15 and 5-3 would be 1/53.
A Recap of Positive Exponents
Before addressing how negative exponents work, here's a quick review of positive exponents. A positive exponent is like a ticker that tells you how many times to multiply 1 by the base number (the full-size number at the bottom of the exponent). So for example, x2 is the same as 1 × x × x (1 multiplied by x twice); y5 is the same as 1 × y × y × y × y × y (1 multiplied by y 5 times); and a = bx would represent 1 multiplied by b x times. You don't have to know what number x or any of the other variables represent; you just need to understand the concept. Once you're comfortable with the idea of positive exponents, you're just one small step away from calculating negative exponents.
Negative Exponents as Division
If a positive exponent represents multiplying the base number by itself, negative exponents represent how many times you'd divide 1 by the base number. So while x2 represents 1 × x × x, x-2 represents 1 ÷ x ÷ x; y5 represents 1 × y × y × y × y × y, and y-5 equals 1 ÷ y ÷ y ÷ y ÷ y ÷ y; and so on. After you work a few of these, you'll start to realize that there's an obvious pattern here. For example, x-2 = 1/x2 and y-5 = 1/y5. So if it makes your calculations easier, you can simply rewrite negative exponents as positive exponent in the denominator of a fraction, with 1 as the numerator.
Working Negative Exponents in Your Calculator
Every calculator's functions are different. But as a general rule any scientific calculator should have an exponent key, usually marked with the carat or ^ symbol. You can use this key to enter any exponent, positive or negative, into the calculator; simply input the base number, hit the ^ key, then input the exponent. If the exponent is negative, use the calculator's negative key, which might look like a minus sign in parentheses: (−).
As you continue your math journey, you'll no doubt encounter zero as an exponent. You can work zero exponents just as you'd calculate any other exponent; all you have to do is remember that a positive number in the exponent represents how many times you multiply 1 by the base number, and a negative number in the exponent represents how many times you divide 1 by the base number. So if you had 50, you'd multiply 1 by 5... zero times. In other words, you're left with 1 on its own. If your teacher tried to trick you by giving you the exponent 5-0, you'd divide 1 by 5 exactly zero times, so you'd be left with 1 on its own again.