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Simplify \(\frac{\sqrt{8^2 \times 4^{n + 1}}}{2^{2n} \t...

Simplify $\frac{\sqrt{8^2 \times 4^{n + 1}}}{2^{2n} \times 16}$

A.

16

B.

8

C.

4

D.

1

View answer & explanation

Correct answer is C

$\frac{\sqrt{8^2 \times 4^{n + 1}}}{2^{2n} \times 16}$

= $\frac{\sqrt{2^{3(2)} \times 2^{2(n + 1)}}}{2^{2n} \times 2^4}$

= $\frac{\sqrt{2^6 \times 2^{2n + 2)}}}{2^{2n} + 4}$

= $\frac{\sqrt{2^6 + 2^{2n + 2)}}}{2^{2n} + 4}$

= $\frac{\sqrt{2^{2n + 8}}}{2^{2n} + 4}$

= $\sqrt{2^{2n + 8} \div 2^{2n} + 4}$

= $\sqrt{2^{2n - 2n} + 8 - 4}$

= $\sqrt{2^4}$

= $\sqrt{16}$

= 4

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