Question

simplify.
$(3x^4)^5(2xy^2)^3$
$?x^{\square}y^{\square}$

Explanation:

Step1: Apply power of a product rule

For \((3x^{4})^{5}\), use \((ab)^n = a^n b^n\) and \((a^m)^n=a^{mn}\):
\(3^5(x^{4})^{5}=243x^{20}\)

For \((2xy^{2})^{3}\), use \((ab)^n = a^n b^n\) and \((a^m)^n=a^{mn}\):
\(2^3x^{3}(y^{2})^{3}=8x^{3}y^{6}\)

Step2: Multiply the two simplified expressions

Multiply coefficients and like bases:
\(243x^{20} \cdot 8x^{3}y^{6}=(243 \cdot 8)x^{20 + 3}y^{6}\)

Calculate \(243 \cdot 8 = 1944\) and \(20 + 3 = 23\).

Answer:

\(1944x^{23}y^{6}\)