Question

pls urgent with explanation not only option​

Answer 1

See the photo to get the answer. thank you

Answer 2

Answer:

Step-by-step explanation:

Given,

$(a^m)^n=a^{{m}^{n}}$

To Find :-

Value of 'm' in terms of 'n'.

How To Do :-

First of all we need to make the bases equal such that by using 'If bases are equal powers also equal'(exponent identity) we can equate the powers and we need to find the value of 'm' in terms of 'n'.

Formula Required :-

1) If bases are equal powers also equal :-

If , cˣ = cᵇ

→ x = b.

2) cˣ/cᵇ = cˣ ⁻ ᵇ

3) (cˣ)ᵇ = cˣᵇ

4) $\sqrt[b]{c} =c^{\dfrac{1}{b}}$

Solution :-

$(a^m)^n=a^{{m}^{n}}$

$\implies a^{mn}=a^{{m}^{n}}$

[ ∴ (cˣ)ᵇ = cˣᵇ ]

Now we can observe that bases are equal , so we can equate the powers also :-

$\implies mn=m^n$

Transposing 'm' in L.H.S to R.H.S :-

$n=\dfrac{m^n}{m}$

$n=m^{n-1}$

[∴ cˣ/cᵇ = cˣ ⁻ ᵇ ]

Transposing (n - 1) to L.H.S :-

$\sqrt[n-1]{n} =m$

$m=n^{\frac{1}{n-1}}$

[ ∴ $\sqrt[b]{c} =c^{\dfrac{1}{b}}$ ]

$\therefore m=n^{\frac{1}{n-1}}$

Hence option '1'