Exponential equation with fractions

Question

Solve $6^{5/2}$ $\left(\dfrac{3}2\right)^{-3/2}$ where i get $6^{5/2}$ *$\dfrac{3^{-3/2}}{2^{-3/2}}\cdot$ which i get to $6^{5/2}$ *$\dfrac{2^{3/2}}{3^{3/2}}\cdot$ which leads to $\dfrac{12^{8/2}}{3^{3/2}}\cdot$ that i get to $4^{5/2}$. Can you show me where this is wrong?

Answer 1

HINT: it is $$\frac{6^{5/2}\cdot 2^{3/2}}{3^{3/2}}=\frac{2^{5/2}\cdot 3^{5/2}\cdot 2^{3/2}}{3^{3/2}}=2^4\cdot 3$$