Answer:
[tex][tex]4608\sqrt{3}[/tex][/tex]
Step-by-step explanation:
1. [tex]\sqrt{96} *\sqrt{6}* 2*\sqrt{6}*4 *\sqrt{6} *4*\sqrt{3}[/tex]
2. [tex]\sqrt{2^{5} *3} \sqrt{6} *2\sqrt{6}*4\sqrt{6}*4\sqrt{3}[/tex] factoring 96
since [tex]\sqrt{2^{5}*3 } = \sqrt{2^{5} } \sqrt{3}[/tex]
3. [tex]\sqrt{2^{5} } \sqrt{3}\sqrt{6} *2\sqrt{6}*4\sqrt{6}*4\sqrt{3}[/tex]
using exponent rule - [tex](a^{b}) ^{c} = a^{bc}[/tex]
[tex]\sqrt{2^{5} } = 2^{5/2}[/tex]
4. [tex]2^{5/2}\sqrt{3}\sqrt{2*3} *2\sqrt{6}*4\sqrt{6}*4\sqrt{3}[/tex]
doing some simple simplification and [tex]4=2^{2}[/tex] and 6=2*3
5. [tex]2^{5/2} \sqrt{3} \sqrt{2} \sqrt{3} *2\sqrt{2} \sqrt{3} *2^{2}\sqrt{2} \sqrt{3}*4\sqrt{3}[/tex]
collecting the roots on one side and applying exponent rule
6. [tex]\sqrt{3} \sqrt{3}\sqrt{3} \sqrt{3}\sqrt{2} \sqrt{2}\sqrt{2} *2^{5/2+1+2+2} \sqrt{3}[/tex]
Applying exponents rule on all [tex]\sqrt{3}[/tex] and [tex]\sqrt{2}[/tex]
7. [tex]2^{1/2+1/2+1/2} *2^{5/2+1+2+2}*3^{1/2+1/2+1/2+1/2+1/2}[/tex]
combining all powers of 2
8. [tex]2^{1/2+1/2+1/2+5/2+1+2+2}*3^{1/2+1/2+1/2+1/2+1/2}[/tex]
Simplifying
9. [tex]2^{9} *3^{2}\sqrt{3}[/tex]
10. [tex]512*9\sqrt{3}[/tex]
11. [tex]4608\sqrt{3}[/tex]
