Extended Powers & Roots

How the lesson starts: Extended Powers & Roots

The Power Factory
Beep boop! Bolt the robot runs the Power Factory. The control panel has strange buttons, like √81 and 7⁰. Press the wrong one and the factory makes spaghetti socks! Today you'll learn what they mean, and why they make sense.
Square roots
A square root asks: what number times itself makes this? 81 tiles make a 9 by 9 square, so √81 = 9. Here are Bolt's pairs. √4 = 2. √9 = 3. √25 = 5. √81 = 9. And √144 = 12, because 12 × 12 = 144.
Why 2⁰ = 1
Why is 2⁰ equal to 1? Watch the pattern. 2³ = 8. Go down one power and divide by 2: 2² = 4. Divide by 2 again: 2¹ = 2. Once more: 2⁰ = 1! So any nonzero number to the zero power is 1. Not 0!