(24m¹⁹m) ÷ (8m⁶ × 2m⁵)

For the first term, $(24m^{19}m)$, combine the $m$ terms using the rule $a^x \cdot a^y = a^{x+y}$:

$$24m^{19}m^1 = 24m^{19+1} = 24m^{20}$$

For the second term, $(8m^6 \times 2m^5)$, multiply the coefficients and combine the $m$ terms:

$$(8 \times 2) \times (m^6 \times m^5) = 16m^{6+5} = 16m^{11}$$

The expression now becomes:

$$24m^{20} \div 16m^{11}$$

Divide the numerical coefficients and the variable terms separately.
Divide the coefficients:

$$\frac{24}{16} = \frac{3 \times 8}{2 \times 8} = \frac{3}{2}$$

Divide the variable terms using the rule $\frac{a^x}{a^y} = a^{x-y}$:

$$\frac{m^{20}}{m^{11}} = m^{20-11} = m^9$$