Final answer:
The statement is true; expression in the lactose operon is high when glucose levels are low and lactose (or its metabolite allolactose) is present, which also applies to the galactose operon.
Step-by-step explanation:
The statement "Expression is high when glucose levels are low and the activating metabolite is present in the lactose operon and in the galactose operon" is true. In the lactose operon, which is also known as the lac operon, maximal expression occurs when two conditions are met: glucose levels are very low or nonexistent, and lactose (whose metabolite is allolactose) is present. Allolactose serves as an inducer, activating the operon by binding to the lac repressor and preventing it from inhibiting transcription of enzymes necessary for lactose metabolism. Additionally, when glucose levels are low, cyclic AMP (cAMP) accumulates and binds to the catabolite activator protein (CAP), further activating transcription of the lac operon.
On a similar note, the galactose operon is regulated in a manner that ensures the cell only metabolizes galactose when it is available and when preferred sources like glucose are not. Though the initial question does not provide detailed information about the galactose operon, it is generally true that operons responsible for metabolizing sugars other than glucose are regulated in a way to favor energy efficiency and prevent wasteful expression of enzymes when the cell's preferred energy source, glucose, is available.