If 44 fsqrt x isqrt x-2561- the value of x is

The correct option is C 4 Given, (4^√(x))^√(x)=256 256 = 4^4 ⇒ (4^√(x))^√(x) = 4^4 ∵ (a^m)^n = (a)^m × n ⇒ (4^√(x)×√(x) = 4^4 ⇒ (4)^x = 4^4 ⇒ x = 4 ...

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Byju's Answer

Standard VIII

Mathematics

Power of a Power

If 44 fsqrt x...

Question

If $(4^{\sqrt{x})^{\sqrt{x}}} = 256$ , the value of x is

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$\sqrt{2}$

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Solution

The correct option is C
4

Given, $(4^{\sqrt{x})^{\sqrt{x}}} = 256$

$256 = 4^{4}$

$\Rightarrow (4^{\sqrt{x})^{\sqrt{x}}} = 4^{4}$

$∵ (a^{m})^{n} = (a)^{m \times n}$

$\Rightarrow (4^{\sqrt{x} \times \sqrt{x}} = 4^{4}$
$\Rightarrow (4)^{x} = 4^{4}$

$\Rightarrow x = 4$

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If (4√x)√x=256, the value of x is

The correct option is C 4 Given, (4√x)√x=256 256 = 44 ⇒(4√x)√x = 44 ∵(am)n = (a)m×n ⇒(4√x×√x = 44 ⇒(4)x = 44 ⇒x = 4

If $(4^{\sqrt{x})^{\sqrt{x}}} = 256$ , the value of x is

The correct option is C
4

Given, $(4^{\sqrt{x})^{\sqrt{x}}} = 256$

$256 = 4^{4}$

$\Rightarrow (4^{\sqrt{x})^{\sqrt{x}}} = 4^{4}$

$∵ (a^{m})^{n} = (a)^{m \times n}$

$\Rightarrow (4^{\sqrt{x} \times \sqrt{x}} = 4^{4}$
$\Rightarrow (4)^{x} = 4^{4}$

$\Rightarrow x = 4$