Question

simplify:
$(2x^{3}y)^{2}(3xy^{2})^{3} = \square$ assume all variables are positive.

Explanation:

Step1: Expand each term via exponent rules

First, apply the power of a product rule \((ab)^n = a^n b^n\) to each factor:
For \((2x^3y)^4\):
\(2^4 \cdot (x^3)^4 \cdot y^4 = 16x^{12}y^4\)
For \((3xy^2)^2\):
\(3^2 \cdot x^2 \cdot (y^2)^2 = 9x^2y^4\)

Step2: Multiply the expanded terms

Multiply the coefficients and combine like variables using \(x^a \cdot x^b = x^{a+b}\):
\(16x^{12}y^4 \cdot 9x^2y^4 = (16 \times 9) \cdot x^{12+2} \cdot y^{4+4}\)

Step3: Compute final values

Calculate the coefficient and simplify exponents:
\(144x^{14}y^8\)

Answer:

\(144x^{14}y^8\)