L.H.S=9^1/3 × 9^1/9 × 9^1/27 × …..∞

=9^{(1/3)+(1/9)+(1/27)+…∞}

The series in the exponent is an infinite geometric series

Whose, a

∴Sum of the series in the exponent

∴L.H.S=9^1/2

=3=R.H.S

Hence, Proved that 9^1/3 × 9^1/9 × 9^1/27 × …..∞ = 3