Question

(\frac{1}{3}(6x^{3}y)^{3}(2x^{5}y^{4}))

Explanation:

Step1: Expand the cubed term

First, apply the power of a product rule: $(ab)^n=a^n b^n$ and power rule: $(a^m)^n=a^{m \cdot n}$ to $(6x^3y)^3$.
$$(6x^3y)^3 = 6^3 \cdot (x^3)^3 \cdot y^3 = 216x^9y^3$$

Step2: Multiply by the fraction

Multiply the expanded term by $\frac{1}{3}$.
$$\frac{1}{3} \cdot 216x^9y^3 = 72x^9y^3$$

Step3: Multiply by the remaining term

Multiply by $2x^5y^4$, using the product rule for exponents: $a^m \cdot a^n = a^{m+n}$.
$$72x^9y^3 \cdot 2x^5y^4 = (72 \cdot 2)x^{9+5}y^{3+4} = 144x^{14}y^7$$

Answer:

$144x^{14}y^7$