Question

Please answer this question.​

Answer 1

Given:

• If $\sf \dfrac {a^{m}}{a^{n}}$ = 1

To find:

• The value of m.

$\:$

Solution:

As we are given the equation:

$\sf \dfrac {a^{m}}{a^{n}}$ = 1

$\bigstar {\mathfrak {\pink {Using\ law\ of \: indices \: \dfrac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}}}}$

$\sf \dfrac {a^{m}}{a^{n}} = 1$

$\sf a^{m - n} = 1$

$\bigstar {\mathfrak {\red {Using\ law\ of \: indices \: {a}^{0} = 1}}}$

$\sf a^{m - n} = {a}^{0}$

$\bigstar {\mathfrak {\orange {On\ equating\ the\ powers\ of\ a}}}$

m-n = 0

So,

m = 0+n

$\boxed {\bf {\blue {m = n}}}$

$\:$

Value of m:

Value of m is n, so option B) n is correct.

Answer 2

Answer:

๑ Here the concept of exponent and powers is used. When bases are same and they are divided then the powers get subtracted. And also any non zero number raised to the power 0 is equal to 1.

Rules used :

$\mathtt{1. \: \pink{a⁰= 1}}\\ \\ \mathtt{2. \: \purple{ \frac{a^{x}}{a^{y}}= a^{x-y}}}$

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Its given that

$\mathtt{ \implies \frac{a^{m}}{a^{n}}= 1} \\ \\ \bull \: \sf{ \underline{ \orange{power \: get \: subtracted}}}\\ \\ \mathtt{ \implies a^{m-n} = 1}\\ \\ \mathtt{ \implies m-n = 0} \\ \\ \mathtt{ \implies \red{m = n}}$

Therefore option B) n is correct.

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