Question

if a^m×a^n= (a^mn), prove that m(n-2) + n(m - 2) = 0.​

Answer 1

Answer:

the answer is below

Step-by-step explanation:

$a^m * a^n = a ^m ^n$

m + n = mn

$m = mn-n$

to prove:

m(n-2) + n(m-2) = 0

mn - 2m + mn - 2n = 0

2 (mn-m-n) = 0

mn-n-m = 0

this is L.H.S

mn = n + m

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

⇒mn - 2m + mn - 2n

⇒n+m+n+m-2m-2n

⇒0

R.H.S = 0

∵ L.H.S = R.H.S,

hence proved

make sure you make a table and then substitute the value of mn

Answer 2

✦✧ANSWER✦✧

Answer:

the answer is below

Step-by-step explanation:

$$a^m * a^n = a ^m ^n$$

m + n = mn

$$m = mn-n$$

to prove:

m(n-2) + n(m-2) = 0

mn - 2m + mn - 2n = 0

2 (mn-m-n) = 0

mn-n-m = 0

this is L.H.S

mn = n + m

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

⇒mn - 2m + mn - 2n

⇒n+m+n+m-2m-2n

⇒0

R.H.S = 0

∵ L.H.S = R.H.S,

hence proved

make sure you make a table and then substitute the value of mn

hope this will help you♥☺