Question

1. $(3x^{4}y^{3})^{4}cdot 2(y^{2})^{3}$

Explanation:

Step1: Apply power of a product rule

For \((3x^{4}y^{3})^{4}\), use \((ab)^n = a^n b^n\) and \((a^m)^n=a^{mn}\). So, \(3^4(x^{4})^{4}(y^{3})^{4}=81x^{16}y^{12}\).
For \(2(y^{2})^{3}\), use \((a^m)^n = a^{mn}\), so \(2y^{6}\).

Step2: Multiply the two expressions

Multiply \(81x^{16}y^{12}\) and \(2y^{6}\). When multiplying like bases, add exponents: \(81\times2\times x^{16}\times y^{12 + 6}=162x^{16}y^{18}\).

Answer:

\(162x^{16}y^{18}\)