If -5n - 125- then 5n-64 - 6251-5251-125

The correct option is C 25 √(5^n) = 125, 5^n/2= 5^3 Comparing, we get n/2 = 3 ⇒ n = 6 Now 5^n√(64)= 5^64^1/n = 5^64^1/6 = 5^(2^6)^1/6 = 5^2^6 ×1/6 = 5^2 = ...

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Byju's Answer

Standard IX

Mathematics

Laws of Exponents for Real Numbers

If √5n = 125,...

Question

If $\sqrt{5^{n}} = 125, t h e n 5^{n \sqrt{64}}$ =

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$\frac{1}{125}$

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625

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$\frac{1}{5}$

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Solution

The correct option is A
25

$\sqrt{5^{n}} = 125, 5^{\frac{n}{2}} = 5^{3} C o m p a r i n g, w e g e t \frac{n}{2} = 3 \Rightarrow n = 6 N o w 5^{n \sqrt{64}} = 5^{64^{\frac{1}{n}}} = 5^{64^{\frac{1}{6}}} = 5^{(2^{6})^{\frac{1}{6}}} = 5^{2^{6 \times \frac{1}{6}}} = 5^{2} = 25$

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Similar questions

Q. If

\sqrt{5^{n}} = 125

, then

=

(a) 25

(b)

\frac{1}{125}

\frac{1}{5}

Q. If

\sqrt{5^{n}} = 125

then find the value of

5^{\sqrt[n]{64}}

Q. If

\sqrt{5^{n}} = 125

then find the value of

5^{\sqrt[n]{64}}

Q. If

{(3^{3})}^{2} = 9^{x} then 5^{x} = ?

(a) 1
(b) 5
(c) 25
(d) 125

If $\sqrt{5^{n}} = 125$ then find the value of $5^{\sqrt[n]{64}}$ .

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If √5n=125,then5n√64 =

The correct option is A 25 √5n=125,5n2=53Comparing, we getn2=3⇒n=6Now5n√64=5641n=56416=5(26)16=526×16=52=25

If $\sqrt{5^{n}} = 125, t h e n 5^{n \sqrt{64}}$ =

The correct option is A
25

$\sqrt{5^{n}} = 125, 5^{\frac{n}{2}} = 5^{3} C o m p a r i n g, w e g e t \frac{n}{2} = 3 \Rightarrow n = 6 N o w 5^{n \sqrt{64}} = 5^{64^{\frac{1}{n}}} = 5^{64^{\frac{1}{6}}} = 5^{(2^{6})^{\frac{1}{6}}} = 5^{2^{6 \times \frac{1}{6}}} = 5^{2} = 25$