Just making sure is economic power exerted through trade perceived as a hard power? or just economic in general is soft power and military power is the only hard power??
If a country is clearly offering trade in return for the recipient country doing something (eg china will only trade with you if you don't recognise the ROC), then that's a 'carrot' and constitutes hard power. Military power is definitely *not* the only hard power - any situation where the country is saying that it will punish or reward a state/group for doing something is hard power.
Soft power on the other hand aims to create a positive image of the state and therefore encourage other states to align their policies with it - eg if I'm a student at a Confucius institute, I'm more likely to hold certain Chinese values in high regard and maybe eventually that'll trickle up into the policy my country has towards China and cause my country to adjust it's policy in such a way as to benefit China. It's much more indirect, and often difficult to see the consequences of. As a further illustration, America is the king of soft power because it has largely succeeded in pushing forward its essential characteristics of 'democracy' and 'freedom' as the ideal other states should strive for. So now, implicit within striving for 'democracy' is striving to be more like America and emulate/complement its policies, which leads to countries being more likely to adopt policies that are beneficial towards America.
Think of soft power as popularity - if I idealise a celebrity and their values, I'm likely to model myself on them; then if I meet that celebrity, I'm more likely to become friends with them, or know how to act in such a way as to make them happy, because we are similar. Basically, China wants to be the Beyoncé of the global political arena.
Hope this helps!! Let me know if any of it is confusing