I was trying to learn "Montagues and Capulets" and I saw this video of someone playing it.Whats she doing with the base? I think she must be using the pedals, but I don't know which one. The sheet music I have doesn't seem to notate any pedals. https://web.media.mit.edu/~mike/scores/prokofiev/montague-capulet/index.pdf
She's using the sustain pedal (the one on the far right). She can do this because, in the opening four measures, only one chord (E minor) is sounding, so there's really nothing in the melody that would clash with other sustained pitches. Measures 5 and 6 are another chord (B minor), but again nothing in the melody will clash with each other.
However, she does change the pedal (that is, she lets up the pedal and immediately presses it back down) every beat 1 and 3. This is largely because those bass notes (the E/G and then D/B) will muddy up the sound if they're both sustained at the same time.
The pedal isn't written in the score, as you say, but it's all but implied with the tenuto markings in the left hand. With the large leaps between each of these beats, it's hard to play these chords tenuto without using the pedal to help create some extra sustain. Notice that she quits using the pedal in m. 9 when beats 2 and 4 are specified as quarter rests.