Simplify: 3x2 sqrt(6x) + 2

Step 1: Start with the given expression.

$\frac{2^{6x-2} \cdot 3^x}{2^{3x-2}}$

Step 2: Apply the quotient of powers rule: $\frac{a^m}{a^n} = a^{m-n}$.

$\frac{2^{6x-2}}{2^{3x-2}} \cdot 3^x = 2^{(6x-2)-(3x-2)} \cdot 3^x$

Step 3: Simplify the exponent.

$(6x-2) - (3x-2) = 6x - 2 - 3x + 2 = 3x$

$2^{3x} \cdot 3^x$

Step 4: Rewrite using power of a power rule.

$2^{3x} = (2^3)^x = 8^x$

$8^x \cdot 3^x$

Step 5: Apply the product of powers rule: $a^m \cdot b^m = (a \cdot b)^m$.

$(8 \cdot 3)^x = 24^x$

** 24^x **