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You are taking a multiple choice test that has 6 questions. Each of the questions has 3 choices, with one correct choice per question. If you select one of these options per question and leave nothing blank, in how many ways can you answer the questions?

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ANSWER

729

EXPLANATION

Given:

6 question with each question having 3 choices.

Desired Outcome:

Number of ways the questions can be answered.

Now,

The sum of the ways to answer each question is equal to the total number of ways to answer all the questions.

That is:

[tex]3^6=3\times3\times3\times3\times3\times3=729[/tex]

Hence, the number of ways the questions can be answered is 729.

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