me da este error al ejecutar npm run dev con nuxt intento instalar el nuxt/webpack pero sigue el error <code> FATAL Module @nuxt/webpack...

Puedes compartir el package.json por favor, el stack del error no dice exactamente porque falla, en este último que compartes ya no esta el error de nuxt/webpack

aqui esta el log

0 info it worked if it ends with ok
1 verbose cli [ 'C:\\Program Files\\nodejs\\node.exe',
1 verbose cli   'C:\\Program Files\\nodejs\\node_modules\\npm\\bin\\npm-cli.js',
1 verbose cli   'run',
1 verbose cli   'dev' ]
2 info using npm@6.7.0
3 info using node@v11.10.1
4 verbose run-script [ 'predev', 'dev', 'postdev' ]
5 info lifecycle vuenuxt@1.0.0~predev: vuenuxt@1.0.0
6 info lifecycle vuenuxt@1.0.0~dev: vuenuxt@1.0.0
7 verbose lifecycle vuenuxt@1.0.0~dev: unsafe-perm in lifecycle true
8 verbose lifecycle vuenuxt@1.0.0~dev: PATH: C:\Program Files\nodejs\node_modules\npm\node_modules\npm-lifecycle\node-gyp-bin;C:\Users\codework\Desktop\vuenuxt\node_modules\.bin;C:\Users\codework\bin;C:\Program Files\Git\mingw64\bin;C:\Program Files\Git\usr\local\bin;C:\Program Files\Git\usr\bin;C:\Program Files\Git\usr\bin;C:\Program Files\Git\mingw64\bin;C:\Program Files\Git\usr\bin;C:\Users\codework\bin;C:\ProgramData\Oracle\Java\javapath;C:\WINDOWS\system32;C:\WINDOWS;C:\WINDOWS\System32\Wbem;C:\WINDOWS\System32\WindowsPowerShell\v1.0;C:\Program Files\Git\cmd;C:\xampp\php;C:\ProgramData\ComposerSetup\bin;C:\Program Files\Microsoft VS Code\bin;C:\WINDOWS\System32\OpenSSH;C:\Program Files\nodejs;C:\Users\codework\AppData\Local\Programs\Python\Python37-32\Scripts;C:\Users\codework\AppData\Local\Programs\Python\Python37-32;C:\Users\codework\AppData\Local\atom\bin;C:\Users\codework\AppData\Roaming\Composer\vendor\bin;C:\Program Files\Microsoft VS Code\bin;C:\Users\codework\AppData\Local\Microsoft\WindowsApps;C:\curl-7.61.1-win64-mingw\bin;C:\Users\codework\AppData\Roaming\npm;C:\Program Files\Git\usr\bin\vendor_perl;C:\Program Files\Git\usr\bin\core_perl
9 verbose lifecycle vuenuxt@1.0.0~dev: CWD: C:\Users\codework\Desktop\vuenuxt
10 silly lifecycle vuenuxt@1.0.0~dev: Args: [ '/d /s /c', 'nuxt' ]
11 silly lifecycle vuenuxt@1.0.0~dev: Returned: code: 1  signal: null
12 info lifecycle vuenuxt@1.0.0~dev: Failed to exec dev script
13 verbose stack Error: vuenuxt@1.0.0 dev: `nuxt`
13 verbose stack Exit status 1
13 verbose stack     at EventEmitter.<anonymous> (C:\Program Files\nodejs\node_modules\npm\node_modules\npm-lifecycle\index.js:301:16)
13 verbose stack     at EventEmitter.emit (events.js:197:13)
13 verbose stack     at ChildProcess.<anonymous> (C:\Program Files\nodejs\node_modules\npm\node_modules\npm-lifecycle\lib\spawn.js:55:14)
13 verbose stack     at ChildProcess.emit (events.js:197:13)
13 verbose stack     at maybeClose (internal/child_process.js:984:16)
13 verbose stack     at Process.ChildProcess._handle.onexit (internal/child_process.js:265:5)
14 verbose pkgid vuenuxt@1.0.0
15 verbose cwd C:\Users\codework\Desktop\vuenuxt
16 verbose Windows_NT 10.0.17134
17 verbose argv "C:\\Program Files\\nodejs\\node.exe" "C:\\Program Files\\nodejs\\node_modules\\npm\\bin\\npm-cli.js" "run" "dev"
18 verbose node v11.10.1
19 verbose npm  v6.7.0
20 error code ELIFECYCLE
21 error errno 1
22 error vuenuxt@1.0.0 dev: `nuxt`
22 error Exit status 1
23 error Failed at the vuenuxt@1.0.0 dev script.
23 error This is probably not a problem with npm. There is likely additional logging output above.
24 verbose exit [ 1, true ]

Vale, crei que el error seria el @ antes del texto, puedes compartir el log completo que te da al final?

y busco la dependencia en node_modules y si esta

si claro lo utilice y no hace nada me sigue dando el mismo error el node y lo reinstale y nada es extraño.

Probaste usando

npm i @nuxt/webpack