In a fractional exponent a^(m/n), what does the denominator n indicate?

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Study for the Algebra 1 Honors End-of-Course Test. Study with flashcards and multiple-choice questions, each question has hints and explanations. Get ready for your exam!

Multiple Choice

In a fractional exponent a^(m/n), what does the denominator n indicate?

Explanation:
The exponent’s denominator shows which root to take. For a^(m/n), you’re taking the n-th root of a^m (or, equivalently, first taking the n-th root of a and then raising to the m-th power). So the n in the denominator indicates the n-th root. For example, 16^(3/4) means the 4th root of 16^3, which is 8. (Equivalently, take the 4th root of 16 to get 2, then raise to the 3rd power to get 8.) Note that with even n, you need a nonnegative base in real numbers; otherwise you’d be dealing with complex values.

The exponent’s denominator shows which root to take. For a^(m/n), you’re taking the n-th root of a^m (or, equivalently, first taking the n-th root of a and then raising to the m-th power). So the n in the denominator indicates the n-th root.

For example, 16^(3/4) means the 4th root of 16^3, which is 8. (Equivalently, take the 4th root of 16 to get 2, then raise to the 3rd power to get 8.)

Note that with even n, you need a nonnegative base in real numbers; otherwise you’d be dealing with complex values.

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