Dividing a^n by a^m with the same base results in the exponent being

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Prepare for the Praxis Middle School Mathematics Exam with quizzes. Study with flashcards and multiple choice questions. Each question provides hints and detailed explanations. Ensure success on your test!

Multiple Choice

Dividing a^n by a^m with the same base results in the exponent being

Explanation:
When you divide expressions with the same base, you subtract the exponents. This comes from the rule a^n ÷ a^m = a^(n−m) because you can think of a^n as a^m times a^(n−m). Using the exponent rule a^n × a^(−m) = a^(n + (−m)) gives a^(n−m). For example, a^7 ÷ a^3 equals a^(7−3) = a^4. If the numerator’s exponent is smaller, like a^2 ÷ a^5, you get a^(2−5) = a^(−3) = 1/a^3. So the exponent is obtained by subtracting the bottom exponent from the top exponent.

When you divide expressions with the same base, you subtract the exponents. This comes from the rule a^n ÷ a^m = a^(n−m) because you can think of a^n as a^m times a^(n−m). Using the exponent rule a^n × a^(−m) = a^(n + (−m)) gives a^(n−m).

For example, a^7 ÷ a^3 equals a^(7−3) = a^4. If the numerator’s exponent is smaller, like a^2 ÷ a^5, you get a^(2−5) = a^(−3) = 1/a^3. So the exponent is obtained by subtracting the bottom exponent from the top exponent.

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