A rational exponent can be rewritten as which form?

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Multiple Choice

A rational exponent can be rewritten as which form?

Explanation:
Rational exponents combine a power and a root. Writing a^(m/n) means you first raise a to the power m, then take the nth root, which is the same as (a^m)^(1/n). In symbols, a^(m/n) = (a^m)^(1/n) = the nth root of a^m. That matches the form described as the nth root of a^m. The other forms describe different operations (for example, the m-th root of a^n equals a^(n/m), which isn’t a^(m/n)), so they don’t represent the same quantity.

Rational exponents combine a power and a root. Writing a^(m/n) means you first raise a to the power m, then take the nth root, which is the same as (a^m)^(1/n). In symbols, a^(m/n) = (a^m)^(1/n) = the nth root of a^m. That matches the form described as the nth root of a^m. The other forms describe different operations (for example, the m-th root of a^n equals a^(n/m), which isn’t a^(m/n)), so they don’t represent the same quantity.

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