What is the result of (a/b)ⁿ?

The expression ((a/b)ⁿ) represents the quantity (a/b) raised to the power of (n). According to the rules of exponents, when a fraction is raised to a power, both the numerator and the denominator are raised to that power. This can be mathematically expressed as:

[

\left(\frac{a}{b}\right)^{n} = \frac{a^{n}}{b^{n}}.

]

This form allows us to see that (a) is raised to the power of (n) in the numerator, while (b) is raised to the power of (n) in the denominator. Therefore, the correct interpretation of ((a/b)ⁿ) is indeed (aⁿ/bⁿ).

Understanding this concept is crucial as it forms a foundation for working with exponents in algebra, especially in simplifying expressions and solving equations. Each of the other choices lacks alignment with this fundamental exponent rule, as they either alter the components or the structure of the original expression inappropriately.