1. (2x+3)^3/2 = 5^3/2 x 3^3/2 2. 6a^-3/2 = 384

(1)
[tex](2x+3)^{3/2}=5^{3/2} \times 3^{3/2} \\ (2x+3)^{3/2}=(5 . 3)^{3/2} \\ (2x+3)^{3/2}=15^{3/2} \\ 2x+3 = 15 \\ 2x = 12 \\ x = 6[/tex]

(2)
[tex]6a^{-3/2} = 384 \\ a^{-3/2} = 64 \\ \frac {1}{a^{3/2}} = 64 \\ a^{3/2} = \frac {1}{64} \\ a^{3/2} = 8^{-2} \\ a^3 = 8^{-1} \\ a^3 = 2^{-3} \\ a^3 = (2^{-1})^3 \\ a = 2^{-1}[/tex]