'strong impact' is a correct and usable phrase in written English. It can be used to describe a powerful effect or influence. For example, "The speech had a strong impact on the audience. ".
"It had a very strong impact.
"Red Storm wasn't offensive but had the same strong impact".
Lagos Soundscapes have a strong impact on the imagination.
The campaign could have a strong impact in Japan.
She usually has a strong impact on them.
This has a strong impact on the national psyche".
Studies show that television can have a strong impact on health.
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MA of Applied Linguistic, Maquarie University, Australia