Question

Apply the properties of exponents to verify that each statement is an identit.

(.2^n+1)/3^n =2 ( 2/3)^n for integer values of n

Answer 1

Answer and explanation :

We have given that the expression
`(2^(n+1))/(3^n)=2* ((2)/(3))^n`

We have to prove L.H.S = R.H.S

Lets take L.H.S

`(2^(n+1))/(3^n)`

It can be written as
`(2^(n+1))/(3^n)=(2^n* 2^1)/(3^n)` ( As in multiplication exponent are added )

So
`(2^n* 2^1)/(3^n)=((2)/(3))^n* 2` = R.H.S

Hence proved