Final answer:
The expression (2a/b^2)^3 is an illustration of the power of a quotient rule. By applying the rule, the expression simplifies to (2a)^3/(b^2)^3, which further simplifies to 8a^3/b^6. Both numerator and denominator are separately raised to the power of three.
Step-by-step explanation:
The expression in question is (2a/b^2)^3. This expression shows a scenario where a quotient is raised to a power. According to the powers of a quotient rule, raising a fraction to an exponent means that both the numerator and the denominator are raised to that exponent separately. Therefore, the given expression can be solved as follows:
(2a/b^2)^3 = (2a)^3/(b^2)^3
Using the rule that raising a power to another power is the same as multiplying the powers:
(2a)^3 = 2^3 × a^3 = 8a^3
(b^2)^3 = b^(2×3) = b^6
Combining these results gives us the final answer:
8a^3/b^6
This demonstrates how the power of a quotient is applied when raising a fractional expression to an exponent.