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The phrase "a much smaller extent" is correct and usable in written English.
It can be used when comparing the degree or level of something in relation to another, indicating that it is significantly less.
Example: "The new policy will affect employee productivity, but only to a much smaller extent than anticipated."
Alternatives: "a significantly lesser degree" or "a considerably reduced extent".
Exact(54)
(Chile's inflation figures have been criticised, too, though to a much smaller extent, and Chile's state statistics institute is far more independent of the government than Argentina's).
However, with the club enjoying a period of footballing transcendence, their organised support has – to a much smaller extent – enjoyed its own renaissance.
Multi-peak profiles were observed in compression in spherodised cementite specimens and to a much smaller extent in the martensite tempered at 400 °C.
They resemble water in their acid base properties but, because of their lower dielectric constants, facilitate processes producing ions to a much smaller extent.
Sintering of supported nickel during sulfidation occurred to a much smaller extent with the niobia-supported catalysts than with the alumina-supported ones.
(2) In the K404E mutant, the influx Kt's for 5-formyltetrahydrofolate and 5-methyltetrahydrofolate were markedly increased, and to a much smaller extent folic acid, as compared to L1210 cells.
Similar(6)
For HI < much smaller extent.
Both bacteria also pose the risk of epidemic spread within the CF community [ 1, 2], with the Bcc being distributed among CF patients to much smaller extent (3 – 30%; [ 3] compared to P. aeruginosa 70 – 80%; [ 1]).
In all dose ranges, a given percentage increase in the tissue concentration of AlSPc gave a much smaller percentage increase in the extent of necrosis for the same light dose, suggesting that selectivity of necrosis between tumour and normal tissue is likely to be much less than the selectivity of retention of the photosensitiser.
In contrast, the iBT straddled the boundary between the two to some extent and involved a much smaller degree of the information reduction that is required in summarizing.
A remarkable result of our studies is that FGF21 increased longevity to a similar extent as caloric restriction while regulating a much smaller set of genes in liver.
More suggestions(15)
a much smaller proportion
a much less extent
a much smaller range
a much smaller degree
a much smaller magnitude
a substantially smaller extent
a much lower extent
a much wider extent
a considerably smaller extent
a much weaker extent
a much smaller part
a much smaller drop
a much smaller station
a much smaller difference
a much smaller role
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com