Question

1. (-4a^3b^2)^2cdot(3a^2b)

Explanation:

Step1: Expand $(-4a^{3}b^{2})^{2}$

Using the power - of - a - product rule $(xy)^n=x^n y^n$ and power - of - a - power rule $(x^m)^n=x^{mn}$, we have $(-4)^2(a^{3})^{2}(b^{2})^{2}=16a^{6}b^{4}$.

Step2: Multiply the result by $3a^{2}b$

Using the product rule of exponents $x^m\cdot x^n = x^{m + n}$, we get $16\times3\times a^{6+2}\times b^{4 + 1}=48a^{8}b^{5}$.

Answer:

$48a^{8}b^{5}$