Final answer:
Option A \((a^0b^3)^4=b^{12}\) is the expression correctly simplified using the laws of exponents as it factors in the multiplication of exponents when a power is raised to another power.
Step-by-step explanation:
The expression that is correctly simplified using the laws of exponents is A. \((a^0b^3)^4=b^{12}\). According to the laws of exponents, when you raise a power to another power, you multiply the exponents. Keeping this in mind, as a^0 equals 1, it does not affect the value of the expression when multiplied. Therefore, \(b^3\) raised to the power of 4 gives \(b^{3 \times 4}\), which simplifies to \(b^{12}\).
The other choices can be quickly disproven:
B. \((a^4b^2)^3\) should be simplified to \(a^{12}b^6\) rather than \(a^7b^5\).
C. \((\frac{a^2}{b^3})^{-3}\) simplifies to \(\frac{a^{-6}}{b^{-9}}\), which is the same as \(\frac{b^9}{a^6}\), and not \(\frac{a^9}{b^6}\).
D. Cannot be evaluated as an expression because it is in the form of a difference, not a single exponentiated quantity.
As an example, think of \((5^3)^4\) as multiplying 3 and 4 to get 12, which gives us \(5^{12}\). This demonstrates how we can apply the rule of raising a power to another power.