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You are taking a multiple-choice test that has 8 questions. Each of the questions has 5 answer choices, with one correct answer per question. If you select one of these choices for each question and leave nothing blank, in how many ways can you answer the questions? You can answer the questions in ◻ ways.

You are taking a multiple-choice test that has 88 questions. Each of the questions has 55 answer choices, with one correct answer per question. If you select one of these choices for each question and leave nothing blank, in how many ways can you answer the questions?\newlineYou can answer the questions in □ \square ways.

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Q. You are taking a multiple-choice test that has 88 questions. Each of the questions has 55 answer choices, with one correct answer per question. If you select one of these choices for each question and leave nothing blank, in how many ways can you answer the questions?\newlineYou can answer the questions in □ \square ways.
  1. Consider First Question: Let's consider the first question. There are 55 possible answers, and you can choose one of them. So, there are 55 ways to answer the first question.
  2. Answer Second Question: Now, for the second question, regardless of how you answered the first question, there are again 55 ways to answer it. This means for the first two questions, there are 5×5=255 \times 5 = 25 ways to answer.
  3. Continue Pattern: Continuing this pattern, for each additional question, you multiply the number of ways to answer by 55. So for 33 questions, there would be 5×5×5=1255 \times 5 \times 5 = 125 ways to answer.
  4. Calculate Total Ways: Since there are 88 questions in total, and each question has 55 answer choices, you would multiply 55 by itself 88 times to find the total number of ways to answer all questions. This is 585^8.
  5. Final Answer: Calculating 585^8, we get 5×5×5×5×5×5×5×5=3906255 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 = 390625. So, there are 390390,625625 ways to answer the 88 questions.

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