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Product Law

If xm = xn,...

Question

If $x^{m} = x^{n}$ , then the value of $m$ is:

A

> n

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B

= n

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C

< n

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D

Cannot be determined

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Solution

The correct option is B $= n$
Given that $x^{m} = x^{n}$
$\Rightarrow x^{m} = x . x . x - - - m$ times.
${= x}^{n} = x . x . x - - - n$ times.
$∵$ Both the sides are equal, the number of times $x$ is multiplied by itself are equal.
$⟹ m = n$

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Similar questions

y = \frac{1}{1 + x^{n - m} + x^{p - m}} + \frac{1}{1 + x^{m - n} + x^{p - n}} + \frac{1}{1 + x^{m - p} + x^{n - p}}

\frac{d y}{d x}

x = e^{m^{n p}}

If ${(\frac{x^{m} \times x^{n}}{x^{p}})}^{q} = x^{K}$ then what is the value of K?

{(\frac{x^{m} \times x^{n}}{x^{p}})}^{q} = x^{K}

then what is the value of K?

y = \frac{1}{1 + x^{n - m} + x^{p - m}} + \frac{1}{1 + x^{m - n} + x^{p - n}} + \frac{1}{1 + x^{m - p} + x^{n - p}}, t h e n \frac{d y}{d x}

y = \frac{1}{1 + x^{n - m} + x^{p - m}} + \frac{1}{1 + x^{m - n} + x^{p - n}} + \frac{1}{1 + x^{m - p} + x^{n - p}}

\frac{d y}{d x}

e^{m^{n^{p}}}

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