If -2n-1024- then - 32n-4-4 - 813927

The correct option is C 9 √(2^n)=1024⇒ (2^n)^1/2=1024=2^10 ⇒ 2^n/2=2^10 Comparing, n/2=10⇒=2×10=20 Now, 3^2(n/4 4 )=3^2(20/4 4 ) =3^2(5 4)=3^2 × 1 =3^2=9 ...

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Byju's Answer

Standard IX

Mathematics

Laws of Exponents for Real Numbers

If √2n=1024, ...

Question

If $\sqrt{2^{n}} = 1024, t h e n 3^{2 (\frac{n}{4} - 4)}$ =

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Solution

The correct option is B
9

$\sqrt{2^{n}} = 1024 \Rightarrow (2^{n})^{\frac{1}{2}} = 1024 = 2^{10}$ $\Rightarrow 2^{\frac{n}{2}} = 2^{10} C o m p a r i n g, \frac{n}{2} = 10 \Rightarrow= 2 \times 10 = 20 N o w, 3^{2 (\frac{n}{4} - 4)} = 3^{2 (\frac{20}{4} - 4)} = 3^{2 (5 - 4)} = 3^{2 \times 1} = 3^{2} = 9$

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If √2n=1024,then 32(n4−4) =

The correct option is B 9 √2n=1024⇒(2n)12=1024=210 ⇒2n2=210Comparing,n2=10⇒=2×10=20Now, 32(n4−4)=32(204−4)=32(5−4)=32×1=32=9

If $\sqrt{2^{n}} = 1024, t h e n 3^{2 (\frac{n}{4} - 4)}$ =