Answer:
n = -½
Explanation:
[tex]\sqrt{\frac{16 }{4^{3}} } = 4^{n}[/tex] Express 16 as 4²
[tex]\sqrt{\frac{4^{2}}{4^{3}}} = 4^{n}[/tex] Do the division
[tex]\sqrt{4^{-1}} = 4^{n[/tex]} Square both sides
[tex]4^{-1} = 4^{2n}[/tex] Take log₄ of both sides
-1 = 2n Divide each side by 2
[tex]n = -\frac{1 }{ 2}[/tex]
===============
Check:
[tex]\sqrt{\frac{16 }{4^{3}} } = 4^{-\frac{ 1}{ 2}}[/tex]
[tex]\sqrt{\frac{16}{ 64}} = \frac{1 }{4^{\frac{1 }{ 2}}}[/tex]
[tex]\sqrt{\frac{1}{4}} = \sqrt{\frac{1}{4}}[/tex]
