This is a common issue when using a globally-installed npm. The npm docs contain a page about it.

They recommend reinstalling node/npm with a version manager (like nvm). This is often a very good option if you are developing something locally. If you do that, this problem will go away. You can stop reading this answer if you want.

They also provide a way to configure npm to put the globally installed items in a directory of your choosing. That is a good option too, if a version manager won't work for you for whatever reason.

Another option they mention is using npx instead of globally installing the tool. I use this one a lot and like it quite a bit, but it does mean that you frequently have to remember to prefix commands you see with npx.

There are two somewhat common options that they do not list. One is to run your install with sudo. This means that any lifecycle scripts will get run as root on your machine. This is generally a bad idea (which is why they don't mention it in the docs), but is very common.

Another option is to chmod your /usr/local/lib/node_modules directory such that you can write to it. This is also a not-great idea in my opinion (which is probably why it too is not mentioned in the docs), but people do it.

In the case of expo-cli and in most developing-something-locally cases, installing with a package manager like nvm is probably the way to go.

although this solution is not the best and the safest solution exists, this worked for me and that make sense because all the problem we had with the errors is the permission problems. so you can use this command and ignore those permission problems :

sudo npm install expo-cli -g --unsafe-perm