81^-1/2 times 81^3/2

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If we apply the rules of exponents that have the same base, we know to add when multiplying. An example of this would be x^3 * x^7 = x^3+7= x^10. In this case, even though we have a number, the same rules apply. So 81^-1/2 times 81^3/2 = 81^-1/2+3/2 = 81^1 = 81. A really complex way to get nowhere!