Não é possível resolver o módulo 'react-dom'

Vi algumas postagens relacionadas a esse tipo de erro. Mas não consegui resolver o meu.

Meu package.json:

"react": "~0.14.7",
"webpack": "^1.12.13",
"react-hot-loader": "^3.0.0-beta.6",
.
.

Estou recebendo o seguinte erro no webpack:

ERROR in ./public/src/main.js
Module not found: Error: Cannot resolve module 'react-dom' in C:\Users\react-example\public\src 
@ ./public/src/main.js 19:16-36

Mas na linha cmd quando eu fiz

npm -v react-dom

Eu recebo 3.10.10. a reação está lá. Mas eu me pergunto por que ainda dá esse erro.

Quando instalei o react-dom através do npm "npm install react-dom" e execute o webpack, recebo os seguintes erros:

ERROR in ./~/react-dom/lib/ReactDOMNullInputValuePropHook.js
Module not found: Error: Cannot resolve 'file' or 'directory' C:\Users\react-example/node_modules/react/lib/ReactComponentTreeHook in C:\Users\react-example\node_modules\react-dom\lib
 @ ./~/react-dom/lib/ReactDOMNullInputValuePropHook.js 13:29-72

ERROR in ./~/react-dom/lib/ReactDOMUnknownPropertyHook.js
Module not found: Error: Cannot resolve 'file' or 'directory' C:\Users\react-example/node_modules/react/lib/ReactComponentTreeHook in C:\Users\react-example\node_modules\react-dom\lib
 @ ./~/react-dom/lib/ReactDOMUnknownPropertyHook.js 15:29-72

ERROR in ./~/react-dom/lib/ReactDOMInvalidARIAHook.js
Module not found: Error: Cannot resolve 'file' or 'directory' C:\Users\react-example/node_modules/react/lib/ReactComponentTreeHook in C:\Users\react-example\node_modules\react-dom\lib
 @ ./~/react-dom/lib/ReactDOMInvalidARIAHook.js 14:29-72

ERROR in ./~/react-dom/lib/ReactDebugTool.js
Module not found: Error: Cannot resolve 'file' or 'directory' C:\Users\react-example/node_modules/react/lib/ReactComponentTreeHook in C:\Users\react-example\node_modules\react-dom\lib
 @ ./~/react-dom/lib/ReactDebugTool.js 16:29-72

Por favor ajude.

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