Question

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

Answer 1

Answer and explanation :

We have given that the expression $\frac{2^{n+1}}{3^n}=2\times (\frac{2}{3})^n$

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

Lets take L.H.S

$\frac{2^{n+1}}{3^n}$

It can be written as $\frac{2^{n+1}}{3^n}=\frac{2^n\times 2^1}{3^n}$ ( As in multiplication exponent are added )

So $\frac{2^n\times 2^1}{3^n}=(\frac{2}{3})^n\times 2$ = R.H.S

Hence proved