If a quotient is raised to an exponent, then the outer exponent can be distributed to the numerator and denominator of the expression.
This means that if you have \((\frac{a}{b})^n\), it can be rewritten as \(\frac{a^n}{b^n}\).
The other options provided do not accurately describe what happens when a quotient is raised to an exponent:
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Exponents of elements with the same base can be subtracted: This applies to situations where you're multiplying or dividing terms with the same base, but not specifically to raising a quotient to a power.
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The components in the numerator and denominator switch places: This is not relevant to raising a quotient to an exponent; it would imply taking the reciprocal, which isn't the same operation.
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All exponents with elements inside the parentheses can be divided by the outer exponent: This is incorrect; exponents within the parentheses are applied to each component evenly, but they are not divided by the outer exponent.
So, the correct statement from your options is indeed the first one.