Answer:

a^m.a^n=a^mn

a^(m+n)=a^mn

m+n=mn

Let it be equation 1

Now

m(n-2)+n(m-2)

=mn-2m+mn-2n

=2mn-2(m+n)

And from equation 1 (m+n)=mn

=2mn-2mn

=0

Step-by-step explanation:

hope it's helpful....

Verified answer

SOLUTION :-

[tex]\small\mathbb\green{a {}^{m} \times a {}^{n} = a {}^{mn}} [/tex]

[tex]\small\mathbb\green{a {}^{(m + n)} = a {}^{mn}}[/tex]

[tex]\small\mathbb\green{m+n=mn}

[/tex]

[tex]\small\mathbb\green{Let \: be \: a \: equation \: 1}[/tex]

[tex]\small\mathbb\green{Now,}[/tex]

[tex]\small\mathbb\green{m(n-2)+(m-2)}[/tex]

[tex]\small\mathbb\green{=mn-2m+mn-2n}[/tex]

[tex]\small\mathbb\green{=2mn-2(m+n)}[/tex]

[tex]\small\mathbb\green{and \: from \: equation \: 1(m + n) = mn}[/tex]

[tex]\small\mathbb\green{= \: 2mn - 2mn}[/tex]

[tex]\small\mathbb\green{= \: 0}[/tex]