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The phrase "analysis of powers" is correct and usable in written English.
It can be used in contexts discussing the distribution and function of powers, often in political or legal frameworks.
Example: "The analysis of powers within the government reveals the checks and balances that prevent any one branch from becoming too powerful."
Alternatives: "examination of powers" or "study of powers".
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In 2001 in The Times, Patricia Cohen found this "a refreshingly systematic analysis of power".
It is based on an analysis of power in a dictatorship and how to break it by withdrawing the obedience of citizens and the key institutions of society".
That pessimistic conclusion, backed by an impressive historical review and a refreshingly systematic analysis of power, is sure to provoke debate among scholars.
Much of the work falls into well-established categories of the avant-garde, exploring themes made familiar by visual artists over the last decade: appropriation, spectatorship, gender issues, postmodernist analysis of power relationships.
In his FT.com Long Room posting, Joules Watt concludes that would correspond to a GDP growth of only 1.5% [year over year] based on his regression analysis of power generation vs. GDP growth.
MST: Technical editor, analysis of power system part, analysis of transient data.
Here Butler and others turn to Michel Foucault's analysis of power.
Governmentality plays a key role in Foucault's analysis of power (Barry 1991; Lemke 2002).
A Lz-transform method is suggested for a short-term reliability analysis of power stations.
This subsection describes the analysis of power consumption that has been conducted for the NC component.
This allows a fairly accurate analysis of power distributions and impulse responses.
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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