It kinda doesn’t make sense.
x¹= x
x² = x*x
x³= x*x*x
etc…
and even with negative numbers you’re still multiplying the number by itself
like (x)-² = 1/x² = 1/(x*x)
In: 1797
For the same reason x * 0 = 0 instead of non-existent. When you “repeat addition” 0 times (you can interpret multiplication as repeated addition), you get the additive identity, which is 0. Repeated addition looks like: 0 + x + x + x + …. When you do x * 3 you take the first four elements of that series, 0 + x + x + x. When you do x * 0, you take the first element of that series, 0.
The same holds with x^0 . When you “repeat multiplication” 0 times (you can interpret exponentiation as repeated multiplication), you get the multiplicative identity, which is 1. Repeated multiplication looks like: 1 * x * x * x * …. Doing x^3 takes the first four elements of that series, and doing x^0 takes the first element of that series.
You can easily understand this in non-mathematical terms:
– Imagine you have a baby and a dog and every time the dog barks, the baby cries 3 times. If the dog barks twice, how many times has the baby cries? 6. That’s because 3 * 2 = 6. If the dog barks zero times, how many times has the baby cried? Zero. That’s because 3 * 0 = 0.
– Similarly, imagine you have a coupon that lets you take 50% off the price, and they don’t limit you to one coupon. How much of the full price do you pay with two coupons? 25%. That’s because 0.5^2 = 0.25. How much of the full price do you pay if you have zero coupons? 100%. That’s because 0.5^0 = 1. Your store would quickly go out of business if you said, “hey, since you have zero coupons, the price is non-existent, so you can’t buy it.”
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