![]() ![]() And when so many kids are criticizing the same stuff the same way almost everywhere, we need to step back and consider that maybe the math curriculum in secondary schools is so flawed that even adolescents can point out the asinine. However, there isn't much you can do for a student who does not see how this will be applicable anywhere else in life. And that's a lot of pressure (especially for that demographic). And it also goes often unsaid that it is also your job to get them ready for 'the test' which will be one of the largest factors that determine their path in life. This may be somewhat disappointing as it is your job to teach these things and hopefully imbue understanding. In fact, instead of doing this in class, you could make this a hand-out for the interested student (this might help the most amount of students). On the other hand, -4 2 represents the additive inverse of 4 2. For example, (-4) 2 means that -4 is to be raised to the second power. 'When a minus sign occurs with exponential notation, a certain caution is in order. Option 2: give them the 'real' definition at the risk of confusing most of them, intriguing a couple, but still telling them that this is how it is because a lot of people wanted those nice properties. If you enter a negative value for x, such as -4, this calculator assumes (-4)n. But I know I always appreciated bluntness from the teacher, so that I could shift my brain into 'as is' mode. ![]() You can lighten this approach by showing them patterns, like the ones already mentioned, which hint at why this should be the way things are. Option 1: just tell them this is how things are and they just need to memorize the rules. So in my opinion, there are two ways to teach exponentiation to high schoolers. 10^9 means: multiply 10 together 9 times. 10^5 means: multiply 10 together 5 times. Start by asking (either rhetorically or Socratically): what is exponentiation meant to mean? It means multiplying by a number multiple times. If you move it to the numerator, its exponent also becomes positive. The same actually works for negative exponents on the bottom. If you have two positive real numbers a and b then b(-a)1/(ba). If you ever see a negative exponent on the top of a fraction, you know that if you flip it to the bottom, itll become positive. That said, this is my personal favourite explanation.) This lesson will cover how to find the power of a negative exponent by using the power rule. Different explanations will work better for different students. Therefore, subtraction of a positive and a negative unlike exponents m and -n m + n. (First of all, I’d echo comment: there not one best way to explain things. To subtract a positive exponents m and negative exponents n, we just connect both the terms by changing the subtraction sign to a positive sign and write the result in the form of m + n. ![]()
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