Question

which expression is equivalent to $(4a^{2}b)^{3}(ab)_{}^{2}$?

$12a^{8}b^{3}$

option 1

$64a^{8}b^{4}$

option 2

$4a^{3}b^{4}$

option 3

$64a^{7}b^{3}$

option 4

Explanation:

Step1: Expand first term via exponent rules

$(4a^2b)^3 = 4^3 \cdot (a^2)^3 \cdot b^3 = 64a^6b^3$

Step2: Expand second term via exponent rules

$(ab^{\frac{1}{2}})^2 = a^2 \cdot (b^{\frac{1}{2}})^2 = a^2b^1 = a^2b$

Step3: Multiply the two expanded terms

$64a^6b^3 \cdot a^2b = 64a^{6+2}b^{3+1} = 64a^8b^4$

Answer:

B. $64a^8b^4$