Question

Question 10(Multiple Choice Worth 5 points)

Answer 1

Answer:  Choice C)  $c^5d^5$

In other words, $(cd)^5 = c^5d^5$

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Explanation:

The outer exponent 5 is "distributed", in a sense, to each term inside the parenthesis. I put it in quotes because we aren't exactly using the distributive property, but you can think of it like that.

The reason why this rule works is because we have five copies of (cd) multiplied together. That means we have five copies of c to get the $c^5$ portion and we also have five copies of d to get the $d^5$ portion.

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This is one way you could show your steps

$(cd)^5 = (cd)(cd)(cd)(cd)(cd)\\\\(cd)^5 = (c*c*c*c*c)(d*d*d*d*d)\\\\(cd)^5 = (c^5)(d^5)\\\\(cd)^5 = c^5d^5$