Measurements of the Branching Fractions of Exclusive Charmless<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">B</mml:mi></mml:math>Meson Decays with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>η</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>or<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ω</mml:mi></mml:math>Mesons

We present the results of searches for B decays to charmless two-body final states containing eta(') or omega mesons, based on 20.7 fb(-1) of data collected with the BABAR detector. We find the branching fractions Beta(B(+)-->eta(')K(+)) = (70+/-8+/-5) x 10(-6), Beta(B(0)-->eta(')K(0)) = (42(+13)(-11) +/- 4) x 10(-6), and Beta(B(+)-->omega pi(+)) = (6.6(+2.1)(-1.8) +/- 0.7) x 10(-6), where the first error quoted is statistical and the second is systematic. We give measurements of four additional modes for which the 90% confidence level upper limits are Beta(B(+)-->eta(')pi(+)) < 12 x 10(-6), Beta(B(+)-->omega K(+)) < 4 x 10(-6), Beta(B(0)-->omega K(0)) < 13 x 10(-6), and Beta(B(0)-->omega pi(0)) < 3 x 10(-6).