We present new Hubble Space Telescope (HST) WFPC2 images of the post-starburst quasar UN J1025-0040, which contains both an active galactic nucleus (AGN) and a 400-Myr-old nuclear starburst of similar bolometric luminosity (10^{11.6} solar luminosities). The F450W and F814W images resolve the AGN from the starburst and show that the bulk of the star light (6 x 10^{10} solar masses) is contained within a central radius of about 600 parsecs, and lacks clear morphological structures at this scale. Equating the point-source light in each image with the AGN contribution, we determined the ratio of AGN-to-starburst light. This ratio is 69% in the red F814W image, consistent with our previous spectral analysis, but about 50% in the blue F450W image whereas we had predicted 76%. The HST images are consistent with previous photometry, ruling out variability (a fading AGN) as a cause for this result. We can explain the new data if there is a previously unknown young stellar population present, 40 Myr or younger, with as much as 10% of the mass of the dominant 400-Myr-old population. This younger starburst may represent the trigger for the current nuclear activity. The multiple starburst ages seen in UN J1025-0040 and its companion galaxy indicate a complex interaction and star-formation history.
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