Are your students confused trying to memorize all the rules for exponents?

Begin with a simple analogy. Just as multiplication made it quicker and easier to express the repeated addition of the same number, so exponents make it quicker and easier to express the repeated multiplication of the same number or variable. Because we understand this concept of exponents, there is no need for memorization of the rules. Teach students how to use simple examples to derive the rules for the product or quotient of powers, the power of a power, and the power of a product or quotient. Use patterns of successive division by the base to build understanding of 1, 0, and negative numbers as exponents. Finally, expect students to be able to derive the rules and assess them on derivation and justification of the rules, not just on application of the rules. You will be giving your students – and their future teachers – the gift of true understanding and mastery.

Some good resources:

Purple Math

Khan Academy exponent properties videos 1, 2, 3

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