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Question : 82 of 86

Marks: +1, -0

If

x^{m^{n}}=(x^{m})^{n}

n=3,

then the value of ' m ' is

3
3
$\sqrt{3}$
Any value

Solution:

Concept:

Equating exponents after simplifying the given equation.

Explanation:

Given:

x^{m^{n}} = (x^{m})^{n}

and

n = 3

.

Since

(x^{m})^{n} = x^{m n}

, the equation becomes

x^{m^{3}} = x^{3m}

.

For

x > 0

and

x \neq 1

, exponents must be equal:

m^{3} = 3m

.

Solve:

m^{3} - 3m = 0

→

m(m^{2} - 3) = 0

→

m = 0

or

m = \pm \sqrt{3}

.

Among the given options,

\sqrt{3}

is listed.

Answer:

m = \sqrt{3}

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