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Write a rule for multiplying two radicals with the same radicand. Justify why your rule works

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torreyem

If you think of the radicand as a product of two factors (here, thinking about 64 as the product of 16 and 4), you can take the square root of each factor and then multiply the roots. The end result is the same, .

This should be a familiar idea. You have applied this rule when expanding expressions such as (ab)x to ax • bx; now you are going to amend it to include radicals as well. Imagine that theexponent x is not an integer but is a unit fraction, like , so that you have the expression . According to the Product Raised to a Power Rule, this can also be written , which is the same as , since fractional exponents can be rewritten as roots. So, for the same reason that , you find that .

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