MCQ
If $\sqrt{2^n}=1024$, then $3^{2(n / 4-4)}$ is equal to
- A3
- ✓9
- C27
- D81
✓
Answer
Correct option: B.
9
(b)
we have, $\sqrt{2^n}=1024 \Rightarrow\left(2^n\right)^{1 / 2}=2^{10} \Rightarrow 2^{n \times 1 / 2}=2^{10} \Rightarrow \frac{n}{2}=10 \Rightarrow n=20$
$\therefore \quad 3^{2\left(\frac{n}{4}-4\right)}=3^{2\left(\frac{20}{4}-4\right)}=3^{2(5-4)}=3^{2 \times 1}=3^2=9$
we have, $\sqrt{2^n}=1024 \Rightarrow\left(2^n\right)^{1 / 2}=2^{10} \Rightarrow 2^{n \times 1 / 2}=2^{10} \Rightarrow \frac{n}{2}=10 \Rightarrow n=20$
$\therefore \quad 3^{2\left(\frac{n}{4}-4\right)}=3^{2\left(\frac{20}{4}-4\right)}=3^{2(5-4)}=3^{2 \times 1}=3^2=9$
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