Question

$(4q^{11})^{3}$ is equivalent to _____. select the correct response: $4q^{14}$ $12q^{33}$ $12q^{14}$ $64q^{33}$ $64q^{14}$

Explanation:

Step1: Apply power of a product rule

$(ab)^n = a^n b^n$, so $(4q^{11})^3 = 4^3 \cdot (q^{11})^3$

Step2: Calculate $4^3$

$4^3 = 4 \times 4 \times 4 = 64$

Step3: Apply power of a power rule

$(q^m)^n = q^{mn}$, so $(q^{11})^3 = q^{11 \times 3} = q^{33}$

Step4: Combine results

$64 \cdot q^{33} = 64q^{33}$

Answer:

64q³³