Question

Square root of 16÷4^3=4^n

Answer 1

Answer:

n = -½

Explanation:

$\sqrt{\frac{16 }{4^{3}} } = 4^{n}$     Express 16 as 4²

$\sqrt{\frac{4^{2}}{4^{3}}} = 4^{n}$     Do the division

$\sqrt{4^{-1}} = 4^{n$}     Square both sides

$4^{-1} = 4^{2n}$    Take log₄ of both sides  

-1 = 2n     Divide each side by 2  

$n = -\frac{1 }{ 2}$

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Check:

$\sqrt{\frac{16 }{4^{3}} } = 4^{-\frac{ 1}{ 2}}$

$\sqrt{\frac{16}{ 64}} = \frac{1 }{4^{\frac{1 }{ 2}}}$

$\sqrt{\frac{1}{4}} = \sqrt{\frac{1}{4}}$