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Examples of the product rule of exponents:
2^1 * 2^2 = 2^(1+2) = 2^3.
10^2 * 10^3 = 10^(2+3) = 10^5.
10^3 * 10^(-6) = 10^(3 + (-6)) = 10^(-3) = 10^(-3).
5^4 * 5^0 = 5^(4+0) = 5
Sometimes when students see the rule they want to write it as 4^2 + 4^3 = 4^5. Can you explain why this does not work?
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