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At a Glance - Exponents

If you're still not sure what exponents are, feel free to travel back in time to our handy exponent guide. We're traveling to whatever planet polynomials are from in this little fantasy of ours, so we don't see why you shouldn't be able to time travel as well. Bring back some baseball stats for us!

In addition to the whole number exponents we talked about earlier, exponents can also be negative, rational, and even irrational.

While they can get freaky, exponents still play by some rules.

Rule #1: The Additive Exponent Rule. Multiplying two powers of a number is the same as adding the exponents.

In symbols, this says that (xa)(xb) = xa + b. Here's a real number example:

(75)(73) = 75 + 3 = 78

Rule #2: The Multiplicative Exponent Rule. If you're taking the power of an exponent (the exponent of something that's already raised to an exponent), then you multiply those exponents together.

In symbols, this is (xa)b = xab. Or, in real numbers, (142)50 = 14100.

Exercise 1

Is 23 × 2 equal to 22 × 22 × 22?

Exercise 2

What is (43 × 45)2?

Exercise 3

Does (ab)c = a(bc)?