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Positive and negative exponents
It's normally a bad idea to hang around with negative people or do negative things, but we think it's OK to associate with negative exponents.
Common Core Standards: 8.EE.A.1
Taking an exponent is basically the act of repeated multiplication. You know how to multiply, right? If so, understanding exponents is completely within your grasp!
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.
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.
Just like whole numbers with exponents, fractions are repeatedly multiplied. If you know how to multiply factions, you're over half way there.
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?
Integers raised to positive integers. Non-zero integers raised to the zero power. 0, -1, and 1 raised to very large positive integers.
Intuition on why a^-b = 1/(a^b) (and why a^0 =1)
Fractional and integer bases raised to positive and negative integer exponents.