how did the empress dowager's support of the Boxers differ from the foreign nations' support of their troops?

The empress support the Boxers to reduce foreign influence in the country. Foreign nations support of their troops were made to spread their influence.

Explanation:

The Boxer Rebellion was  initiated by a group of people who called themselves Yìhéquán. The rebellion was made as a form of protest toward western government who tried to control China with their foreign influence.

Empress Dowager Cixi Vowed her support for the rebellion by Issuing an Imperial Decree declaring and declared a war to foreign powers.  In response to this, Western power formed an alliance to fought of the rebellion.  They wanted the rebellion gone because it pose a threat for their plan to obtain a leverage on trades with Chinese traders.

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(b) britain had a much larger navy than the u.s.

(d) the u.s. had a small army compared to britain.