Which of the following expressions is equivalent to (4a^2b)^3(ab)^3?
a. 64a^9b^6
b. 12a^7b^6
c. 64a^7b^9
d. 16a^6b^6
4^3a^6b^3 * a^3b^3
= 64a^9b^6
= (a)
To find the equivalent expression to (4a^2b)^3(ab)^3, we need to simplify the expression by applying the rules of exponentiation.
First, let's simplify (4a^2b)^3. To raise a power to a power, we multiply the exponents. In this case, we have (4^3)(a^2)^3(b^1)^3, which simplifies to 64a^6b^3.
Next, let's simplify (ab)^3. To raise a product to a power, we raise each factor to that power. In this case, we have (a^1b^1)^3, which simplifies to a^3b^3.
Now, we have (64a^6b^3)(a^3b^3). To multiply these two expressions, we multiply the coefficients (64 and 1) and add the exponents of the variables. This results in 64a^9b^6.
Therefore, the equivalent expression to (4a^2b)^3(ab)^3 is 64a^9b^6, which is option a.