expression
there is no way that ...; it is impossible that ...; cannot possibly ...
A strong negative judgment by the speaker that something is impossible, unreasonable, or cannot be true. Commonly follows a plain-form verb, adjective, or noun phrase.
子どもがそんな重い荷物を一人で運べるわけがない。
There is no way a child could carry such heavy luggage alone.
彼がそんな約束を忘れるわけがない。
He could not possibly forget a promise like that.
expression, i-adjective
Adjectival use meaning that something presents no difficulty. This can be confused with the much more frequent grammar pattern 'there is no way that ...', so context such as 彼には or そのくらいなら is important.
そのくらいの暗算なら、彼にはわけがない。
Mental arithmetic at that level is easy for him.
慣れれば、この作業はわけがない。
Once you get used to it, this task is no trouble.
Also means that something cannot be true, but it often emphasizes expectation or evidence; わけがない can sound more forceful or dismissive.
A shorter adjectival form often used for 'easy' or 'no problem'; わけがない is also a grammar pattern meaning 'there is no way that ...'.
Means 'impossible' or 'unbelievable' as an adjective/exclamation; わけがない is more of a sentence-ending explanatory pattern.
From 訳 meaning 'reason, circumstances' plus the subject marker が and ない 'not exist'. The core idea is literally 'there is no reason/way'; the 'easy' sense can be understood as 'there is no difficulty or complication.'