MCQ
If $\sqrt{2^\text{n}}=1024,$ then $3^{2\Big(\frac{\text{n}}{4}-4\Big)}=$
- A$3$
- ✓$9$
- C$27$
- D$81$
✓
Answer
Correct option: B.
$9$
We have to find $3^{2\Big(\frac{\text{n}}{4}-4\Big)}$
Given $\sqrt{2^\text{n}}=1024$
$\sqrt{2^\text{n}}=2^\text{10}$
$2^{\text{n}\times\frac{1}{2}}$
Equating powers of rational exponents we get
$\text{n}\times\frac{1}{2}=10$
$\text{n}=10\times2$
$\text{n}=20$
Substituting in $3^{2\Big(\frac{\text{n}}{4}-4\Big)}$ we get
$3^{2\Big(\frac{\text{n}}{4}-4\Big)}=3^{2\Big(\frac{20}{4}-4\Big)}$
$=3^{2(5-4)}$
$=3^{2\times1}$
$=9$
Hence the correct choice is $b.$
Given $\sqrt{2^\text{n}}=1024$
$\sqrt{2^\text{n}}=2^\text{10}$
$2^{\text{n}\times\frac{1}{2}}$
Equating powers of rational exponents we get
$\text{n}\times\frac{1}{2}=10$
$\text{n}=10\times2$
$\text{n}=20$
Substituting in $3^{2\Big(\frac{\text{n}}{4}-4\Big)}$ we get
$3^{2\Big(\frac{\text{n}}{4}-4\Big)}=3^{2\Big(\frac{20}{4}-4\Big)}$
$=3^{2(5-4)}$
$=3^{2\times1}$
$=9$
Hence the correct choice is $b.$
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