Which expression represents (a/b)^m?

Which expression represents (a/b)^m?

• A. a^m / b^m
• B. a^m b^m
• C. m/(ab)
• D. a / (b^m)

Answer: (A)

The expression \((a/b)^m\) uses the properties of exponents to show how a fraction raised to a power can be split into separate terms. Specifically, when a fraction is raised to a power, both the numerator and the denominator are raised to that same power. Thus, \((a/b)^m\) can be rewritten by applying the exponent to both \(a\) and \(b\). This gives us \(a^m\) as the new numerator and \(b^m\) as the new denominator, resulting in the expression \(a^m / b^m\). This adheres to the exponent rule which states that \((x/y)^n = x^n / y^n\) for any numbers \(x\), \(y\), and exponent \(n\). Therefore, the correct representation of \((a/b)^m\) is \(a^m / b^m\).

The expression ((a/b)^m) uses the properties of exponents to show how a fraction raised to a power can be split into separate terms. Specifically, when a fraction is raised to a power, both the numerator and the denominator are raised to that same power.

Thus, ((a/b)^m) can be rewritten by applying the exponent to both (a) and (b). This gives us (a^m) as the new numerator and (b^m) as the new denominator, resulting in the expression (a^m / b^m).

This adheres to the exponent rule which states that ((x/y)^n = x^n / y^n) for any numbers (x), (y), and exponent (n). Therefore, the correct representation of ((a/b)^m) is (a^m / b^m).