If you're seeing this message, it means we're having trouble loading external resources for Khan Academy.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Exponents with negative bases

4 videos
2 skills
If you think about it, exponents is simply repeated multiplication. Knowing that, we can apply what we already know about multiplying negative numbers. Exponents with negative and zero bases are treated differently, as well as power of zero exponents. Order of operations will help us make sense of those circumstances.

Exponents with negative bases

VIDEO 4:30 minutes
Apply what we know about negative numbers to determine how negative bases with exponents are affected, and what patterns develop. We'll also learn how order of operations affect the pattern.

Powers of 1 and 0

VIDEO 6:08 minutes
Let's see what happens with bases to the zero power, plus we'll reinforce the patterns of applying exponents to postive and negative bases.

Powers of zero

VIDEO 4:15 minutes
We know that any non-zero number to the zero power equals one. We also know that zero to any non-zero exponent equals one. What happens when you have zero to the zero power?

Raising a number to the 0 and 1st power

VIDEO 5:07 minutes
The progression of powers from zero to any non-zero number follows a pattern and can be logically explained. After watching this, it will make sense why any non-zero number to the zero power equals one.

Positive and zero exponents with positive and negative bases

PRACTICE PROBLEMS
Integers raised to positive integers. Non-zero integers raised to the zero power. 0, -1, and 1 raised to very large positive integers.