Step 1: Understand the meaning of the idiom "by leaps and bounds."
The idiom "by leaps and bounds" means to progress or increase very quickly or rapidly. It conjures an image of large, quick jumps or movements.
Step 2: Analyze the context of the sentence.
The sentence states, "He got fame by leaps and bounds," implying that his fame increased at a fast pace.
Step 3: Evaluate each option based on the idiom's meaning.
(1) slowly: This is the opposite of the idiom's meaning.
(2) silently: The idiom does not relate to the sound or lack thereof.
(3) surprisingly: While rapid progress can be surprising, "surprisingly" is not the direct meaning of "by leaps and bounds." The primary meaning is about speed of progress.
(4) rapidly: This perfectly matches the meaning of "by leaps and bounds," indicating very fast progress or increase.
Step 4: Conclude the correct option.
The correct option that represents the meaning of "by leaps and bounds" is "rapidly."
$$(4) rapidly$$