Question

Question 10(Multiple Choice Worth 5 points)

(01.02 LC)
Which of the following is equivalent to (cd)5?
Oc5d
Ocd5
Oc5d5
O 5cd

Answer 1

Answer: Choice C)
`c^5d^5`

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

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Step-by-step 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\\\\`