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The phrase "a much higher extent" is correct and usable in written English.
It can be used when comparing the degree or level of something in relation to another.
Example: "The new policy will impact employee productivity to a much higher extent than the previous one."
Alternatives: "a significantly greater degree" or "a far larger scale".
Exact(27)
Embankment reduced ANPP and high defoliation increased ANPP with respect to low defoliation frequency in the control paddock, to a much higher extent in the wet season.
While these percentages may be affected by cohort and macroeconomic conditions, the key message is clear enough: older Europeans who leave a career job move directly into retirement to a much higher extent than older Americans.
In the process of model selection, it became evident that the geographic location of observations affected larva density to a much higher extent than the causal predictors CTH and DWT (Table 2).
In contrast to this, SIV Nef interacts with CD3 to a much higher extent as Nef of HIV-1 does.
Compared to lymphocyte/monocytes fractions and macrophage fractions the expression of CXCL8_L2 in the HK granulocytes could be stimulated with LPS to a much higher extent, both in fold expression and even more in absolute terms.
Since substantial quantities of acylated ghrelin are made in a human erythroleukemia (HEL) cell line [8], [9], and since HEL cell ghrelin is acylated to a much higher extent than stomach ghrelin [8], we reasoned that HEL cells must possess enzymatic activity capable of transferring fatty acids to ghrelin.
Similar(33)
However, all isolates from the 7th and 11th culture showed a much faster rate and much higher extent of D-xylose uthanzaTMB3400an TMB3400.
Signal reduction is markedly eradicated by opening a reversible skin-flap in the light path, which increases the detection sensitivity at much higher extent [13].
Moreover these effects go beyond the capacity of syndecan-1 to bind cell-surface receptors, as the expression of downstream effectors was also influenced, often at much higher extent than the syndecan-1 itself, involving ERK/MAPK, Akt, and p38/MAPK signaling cascades and MYC, JNK, JUN, and ETS-1 expression as downstream transcription factors [ 32].
These findings indicated that the β- and γ-cyclodextrin complexes had a much higher rate and extent of bioavailability compared to Artemisinin 250®.
The dnaK transcription levels are induced to a smaller extent, but from a much higher reference level at 30°C.
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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