(Answer is below)
Let's solve this step-by-step.
1. Prime factorization of 384.
[tex]=\sqrt{2^7\times3}[/tex]
2. Apply the exponent rule. (Formula: [tex]a^b^+^c=a^b\times a^c[/tex])
[tex]=\sqrt{2^6\times2\times2\times3}[/tex]
3. Apply the radical rule. (Formula: [tex]\sqrt{ab} =\sqrt{a}\sqrt{b}[/tex] or [tex]a\geq 0,b\geq 0[/tex])
[tex]=\sqrt{2^6} \sqrt{2\times3}[/tex]
3a. Solve 2 to the 6th power.
[tex]\sqrt{2\times2\times2\times2\times2\times2} =8[/tex]
4. Multiply 2 by 3. (Note: Put the 8 in your final answer)
[tex]\sqrt{2\times3} =8\sqrt{6}[/tex]
Your answer is: [tex]8\sqrt{6}[/tex]
Let me know if you have any questions.
~ Lily, from Brainly.
