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Let's take 2^3 * 2^5, we know that we can just add the numbers in the exponent to get 2^8. We can extend this, for example what would 2^3 * 2^0 be? If we want o
by conradludgate 6y ago
Let's take 2^3 * 2^5, we know that we can just add the numbers in the exponent to get 2^8. We can extend this, for example what would 2^3 * 2^0 be? If we want our rule to be consistent, it would be 2^3, implying that 2^0 = 1.
This works fine for all numbers except for 0. Like you pointed out, 0^5 = 0, 0^1 = 0, so it would make sense that 0^0 = 0? but if x^0 = 1, we have an issue.
- badrabbit 6y agoWhy is x^0=1? How can something be generated out of any equation where the only number is 0 (nothing)
- conradludgate 6y ago> We can extend this, for example what would 2^3 * 2^0 be? If we want our rule to be consistent, it would be 2^3, implying that 2^0 = 1 replace 2 with x. Another way to see it is 2^2 = 4 = 8 / 2 = 2^3 / 2 2^1 = 2 = 4 / 2 = 2^2 / 2 2^0 = ? how about 2^1 / 2 = 1 Again, replace 2 with x and the same follows. With this example though, when x = 0, it's obvious that it no longer works since 0^0 would be 0^1 / 0 = 0/0