diff --git a/package.json b/package.json
index e37cdc7..d94d5bf 100644
--- a/package.json
+++ b/package.json
@@ -26,8 +26,9 @@
         "compile:src": "tsc -p src",
         "lint:codegen": "tslint -p codegen/tsconfig.json -c tslint.json",
         "lint:src": "tslint -p src/tsconfig.json -c tslint.json",
-        "lint:types": "./scripts/check-typings.sh",
-        "lint": "npm-run-all -p lint:codegen lint:src lint:types",
+        "lint:dist": "./scripts/check-typings.sh",
+        "lint:types": "dtslint test/types",
+        "lint": "npm-run-all -p lint:codegen lint:src lint:dist lint:types",
         "node:codegen": "node codegen/dist/emit",
         "test": "jest --config jest.config.json",
         "prepack": "yarn build",
@@ -36,6 +37,7 @@
     "devDependencies": {
         "@types/jest": "^22.2.3",
         "@types/node": "^8.10.16",
+        "dtslint": "^0.3.0",
         "jest": "^22.4.3",
         "npm-run-all": "^4.1.3",
         "prettier": "^1.12.1",
diff --git a/src/exponent/exponentArithmetic.ts b/src/exponent/exponentArithmetic.ts
index e3be4fe..2f9f86c 100644
--- a/src/exponent/exponentArithmetic.ts
+++ b/src/exponent/exponentArithmetic.ts
@@ -4,6 +4,8 @@ import { DivideExponents } from "./generated/division";
 import { Exponent } from "./generated/exponent";
 import { MultiplyExponents } from "./generated/multiplication";
 
+export type NonZeroExponent = Exclude<Exponent, 0>;
+
 type SubtractExponents<L extends Exponent, R extends Exponent> = AddExponents<L, Negative<R>>;
 type Negative<N extends Exponent> = MultiplyExponents<N, -1>;
 
diff --git a/src/measure/unitTypeArithmetic.ts b/src/measure/unitTypeArithmetic.ts
index 8fed632..3b66819 100644
--- a/src/measure/unitTypeArithmetic.ts
+++ b/src/measure/unitTypeArithmetic.ts
@@ -5,6 +5,7 @@ import {
     Exponent,
     MultiplicandOf,
     MultiplyExponents,
+    NonZeroExponent,
     ProductOf,
 } from "../exponent";
 
@@ -50,9 +51,9 @@ export interface BaseUnit<N extends Exponent> {
 // Roots
 
 /** Returns the nth root of a unit. This is the inverse scalar multiple of the dimension vector. */
-export type NthRootUnit<U extends Unit, N extends Exponent> = StripZeroes<
-    { [Dim in keyof U]: DivideExponents<GetExponent<U, Dim>, N> }
->;
+export type NthRootUnit<U extends Unit, N extends NonZeroExponent> = 1 extends N
+    ? U
+    : { [Dim in keyof U]: DivideExponents<GetExponent<U, Dim>, N> };
 
 /** A type that is assignable from all units whose Nth root does not produce an error. */
 export interface RadicandUnit<N extends Exponent> {
@@ -68,4 +69,4 @@ type StripZeroes<U extends Unit> = { [Dim in NonZeroKeys<U>]: U[Dim] };
 type NonZeroKeys<U extends Unit> = { [Dim in keyof U]: NonNullable<U[Dim]> extends 0 ? never : Dim }[keyof U];
 
 /** Get the exponent at a given dimension of a unit, or 0 if that dimension is undefined */
-type GetExponent<U extends Unit, D> = D extends keyof Unit ? (undefined extends U[D] ? 0 : NonNullable<U[D]>) : 0;
+export type GetExponent<U extends Unit, D> = D extends keyof U ? NonNullable<U[D]> : 0;
diff --git a/src/measure/unitValueArithmetic.ts b/src/measure/unitValueArithmetic.ts
index 5684c03..3f7dcd3 100644
--- a/src/measure/unitValueArithmetic.ts
+++ b/src/measure/unitValueArithmetic.ts
@@ -1,4 +1,4 @@
-import { Exponent } from "../exponent";
+import { Exponent, NonZeroExponent } from "../exponent";
 import {
     BaseUnit,
     DivideUnits,
@@ -70,7 +70,7 @@ export function exponentiateUnit<U extends BaseUnit<N>, N extends Exponent>(
     return expAndRootImpl(unit, exponent => exponent * power);
 }
 
-export function nthRootUnit<U extends RadicandUnit<N>, N extends Exponent>(
+export function nthRootUnit<U extends RadicandUnit<N>, N extends NonZeroExponent>(
     unit: UnitWithSymbols<U>,
     root: N,
 ): UnitWithSymbols<NthRootUnit<U, N>> {
diff --git a/test/types/index.d.ts b/test/types/index.d.ts
new file mode 100644
index 0000000..38e99dd
--- /dev/null
+++ b/test/types/index.d.ts
@@ -0,0 +1 @@
+// TypeScript Version: 2.9
diff --git a/test/types/measuresErrors.ts b/test/types/measuresErrors.ts
new file mode 100644
index 0000000..a58fc3e
--- /dev/null
+++ b/test/types/measuresErrors.ts
@@ -0,0 +1,16 @@
+import { Area, Measure, Volume } from "safe-units";
+
+Volume.times(Volume); // $ExpectError
+const volumeInverse = Volume.inverse();
+Volume.over(volumeInverse); // $ExpectError
+
+Volume.plus(Area); // $ExpectError
+Area.minus(Volume); // $ExpectError
+
+const s = Volume.squared; // $ExpectType never
+const c = Area.cubed; // $ExpectType never
+Area.toThe(4); // $ExpectType never
+Volume.toThe(-2); // $ExpectType never
+
+Measure.sqrt(Volume); // $ExpectError
+Measure.cbrt(Area); // $ExpectError
diff --git a/test/types/measuresValid.ts b/test/types/measuresValid.ts
new file mode 100644
index 0000000..2ae77ef
--- /dev/null
+++ b/test/types/measuresValid.ts
@@ -0,0 +1,26 @@
+import { Acceleration, kilograms, Measure, meters, newtons, seconds, Velocity } from "safe-units";
+
+Measure.dimension("x"); // $ExpectType GenericMeasure<number, { x: 1; }>
+
+const m = meters; // $ExpectType GenericMeasure<number, { length: 1; }>
+const s = seconds; // $ExpectType GenericMeasure<number, { time: 1; }>
+const n = newtons; // $ExpectType GenericMeasure<number, StripZeroes<{ length: 1; time: -2; mass: 1; }>>
+
+const a = newtons.over(kilograms); // $ExpectType GenericMeasure<number, StripZeroes<{ length: 1; time: -2; mass: 0; }>>
+const accel: Acceleration = a; // $ExpectType GenericMeasure<number, StripZeroes<{ length: 1; time: -2; mass: 0; }>>
+
+const absement = meters.times(seconds); // $ExpectType GenericMeasure<number, StripZeroes<{ length: 1; time: 1; }>>
+const velocity = meters.over(seconds); // $ExpectType GenericMeasure<number, StripZeroes<{ length: 1; time: -1; }>>
+
+meters.plus(meters); // $ExpectType GenericMeasure<number, { length: 1; }>
+meters.minus(meters); // $ExpectType GenericMeasure<number, { length: 1; }>
+meters.negate(); // $ExpectType GenericMeasure<number, { length: 1; }>
+meters.scale(2); // $ExpectType GenericMeasure<number, { length: 1; }>
+
+velocity.squared(); // $ExpectType GenericMeasure<number, { length: 2; time: -2; }>
+absement.cubed(); // $ExpectType GenericMeasure<number, { length: 3; time: 3; }>
+absement.inverse(); // $ExpectType GenericMeasure<number, { length: -1; time: -1; }>
+velocity.toThe(0); // $ExpectType GenericMeasure<number, {}>
+
+Measure.sqrt(velocity.toThe(-4)); // $ExpectType GenericMeasure<number, { length: -2; time: 2; }>
+Measure.cbrt(absement.toThe(3)); // $ExpectType GenericMeasure<number, { length: 1; time: 1; }>
diff --git a/test/types/tsconfig.json b/test/types/tsconfig.json
new file mode 100644
index 0000000..ddd0445
--- /dev/null
+++ b/test/types/tsconfig.json
@@ -0,0 +1,16 @@
+{
+    "extends": "../../tsconfig.base.json",
+    "compilerOptions": {
+        "declaration": true,
+        "strict": true,
+        "noImplicitAny": true,
+        "strictNullChecks": true,
+        "strictFunctionTypes": true,
+        "noImplicitThis": true,
+        "alwaysStrict": true,
+        "noUnusedLocals": false,
+        "lib": ["es5"],
+        "baseUrl": ".",
+        "paths": { "safe-units": ["../../src"] }
+    }
+}
\ No newline at end of file
diff --git a/test/types/tslint.json b/test/types/tslint.json
new file mode 100644
index 0000000..42701ce
--- /dev/null
+++ b/test/types/tslint.json
@@ -0,0 +1,6 @@
+{
+    "extends": "dtslint/dtslint.json",
+    "rules": {
+        "no-useless-files": false
+    }
+}
\ No newline at end of file
diff --git a/yarn.lock b/yarn.lock
index 93a0af1..8a6cddd 100644
--- a/yarn.lock
+++ b/yarn.lock
@@ -24,6 +24,11 @@
   version "8.10.16"
   resolved "https://registry.yarnpkg.com/@types/node/-/node-8.10.16.tgz#96fadb371748845a0c8ea970a565330efb0a67d5"
 
+"@types/parsimmon@^1.3.0":
+  version "1.10.0"
+  resolved "https://registry.yarnpkg.com/@types/parsimmon/-/parsimmon-1.10.0.tgz#ffb81cb023ff435a41d4710a29ab23c561dc9fdf"
+  integrity sha512-bsTIJFVQv7jnvNiC42ld2pQW2KRI+pAG243L+iATvqzy3X6+NH1obz2itRKDZZ8VVhN3wjwYax/VBGCcXzgTqQ==
+
 abab@^1.0.4:
   version "1.0.4"
   resolved "https://registry.yarnpkg.com/abab/-/abab-1.0.4.tgz#5faad9c2c07f60dd76770f71cf025b62a63cfd4e"
@@ -85,6 +90,11 @@ ansi-styles@^3.2.0, ansi-styles@^3.2.1:
   dependencies:
     color-convert "^1.9.0"
 
+any-promise@^1.0.0, any-promise@^1.3.0:
+  version "1.3.0"
+  resolved "https://registry.yarnpkg.com/any-promise/-/any-promise-1.3.0.tgz#abc6afeedcea52e809cdc0376aed3ce39635d17f"
+  integrity sha1-q8av7tzqUugJzcA3au0845Y10X8=
+
 anymatch@^1.3.0:
   version "1.3.2"
   resolved "https://registry.yarnpkg.com/anymatch/-/anymatch-1.3.2.tgz#553dcb8f91e3c889845dfdba34c77721b90b9d7a"
@@ -771,6 +781,13 @@ define-property@^2.0.2:
     is-descriptor "^1.0.2"
     isobject "^3.0.1"
 
+definitelytyped-header-parser@Microsoft/definitelytyped-header-parser#production:
+  version "0.0.0"
+  resolved "https://codeload.github.com/Microsoft/definitelytyped-header-parser/tar.gz/6ff181ecd781706f200f8a780b0133a85fd0a69f"
+  dependencies:
+    "@types/parsimmon" "^1.3.0"
+    parsimmon "^1.2.0"
+
 delayed-stream@~1.0.0:
   version "1.0.0"
   resolved "https://registry.yarnpkg.com/delayed-stream/-/delayed-stream-1.0.0.tgz#df3ae199acadfb7d440aaae0b29e2272b24ec619"
@@ -810,6 +827,17 @@ domexception@^1.0.0:
   dependencies:
     webidl-conversions "^4.0.2"
 
+dtslint@^0.3.0:
+  version "0.3.0"
+  resolved "https://registry.yarnpkg.com/dtslint/-/dtslint-0.3.0.tgz#918e664a6f7e1f54ba22088daa2bc6e64a6001c1"
+  integrity sha512-3oWL8MD+2nKaxmNzrt8EAissP63hNSJ4OLr/itvNnPdAAl+7vxnjQ8p2Zdk0MNgdenqwk7GcaUDz7fQHaPgCyA==
+  dependencies:
+    definitelytyped-header-parser Microsoft/definitelytyped-header-parser#production
+    fs-promise "^2.0.0"
+    strip-json-comments "^2.0.1"
+    tslint "^5.9.1"
+    typescript next
+
 duplexer@^0.1.1, duplexer@~0.1.1:
   version "0.1.1"
   resolved "https://registry.yarnpkg.com/duplexer/-/duplexer-0.1.1.tgz#ace6ff808c1ce66b57d1ebf97977acb02334cfc1"
@@ -1112,12 +1140,30 @@ fs-extra@6.0.0:
     jsonfile "^4.0.0"
     universalify "^0.1.0"
 
+fs-extra@^2.0.0:
+  version "2.1.2"
+  resolved "https://registry.yarnpkg.com/fs-extra/-/fs-extra-2.1.2.tgz#046c70163cef9aad46b0e4a7fa467fb22d71de35"
+  integrity sha1-BGxwFjzvmq1GsOSn+kZ/si1x3jU=
+  dependencies:
+    graceful-fs "^4.1.2"
+    jsonfile "^2.1.0"
+
 fs-minipass@^1.2.5:
   version "1.2.5"
   resolved "https://registry.yarnpkg.com/fs-minipass/-/fs-minipass-1.2.5.tgz#06c277218454ec288df77ada54a03b8702aacb9d"
   dependencies:
     minipass "^2.2.1"
 
+fs-promise@^2.0.0:
+  version "2.0.3"
+  resolved "https://registry.yarnpkg.com/fs-promise/-/fs-promise-2.0.3.tgz#f64e4f854bcf689aa8bddcba268916db3db46854"
+  integrity sha1-9k5PhUvPaJqovdy6JokW2z20aFQ=
+  dependencies:
+    any-promise "^1.3.0"
+    fs-extra "^2.0.0"
+    mz "^2.6.0"
+    thenify-all "^1.6.0"
+
 fs.realpath@^1.0.0:
   version "1.0.0"
   resolved "https://registry.yarnpkg.com/fs.realpath/-/fs.realpath-1.0.0.tgz#1504ad2523158caa40db4a2787cb01411994ea4f"
@@ -1983,6 +2029,13 @@ json5@^0.5.1:
   version "0.5.1"
   resolved "https://registry.yarnpkg.com/json5/-/json5-0.5.1.tgz#1eade7acc012034ad84e2396767ead9fa5495821"
 
+jsonfile@^2.1.0:
+  version "2.4.0"
+  resolved "https://registry.yarnpkg.com/jsonfile/-/jsonfile-2.4.0.tgz#3736a2b428b87bbda0cc83b53fa3d633a35c2ae8"
+  integrity sha1-NzaitCi4e72gzIO1P6PWM6NcKug=
+  optionalDependencies:
+    graceful-fs "^4.1.6"
+
 jsonfile@^4.0.0:
   version "4.0.0"
   resolved "https://registry.yarnpkg.com/jsonfile/-/jsonfile-4.0.0.tgz#8771aae0799b64076b76640fca058f9c10e33ecb"
@@ -2244,6 +2297,15 @@ ms@2.0.0:
   version "2.0.0"
   resolved "https://registry.yarnpkg.com/ms/-/ms-2.0.0.tgz#5608aeadfc00be6c2901df5f9861788de0d597c8"
 
+mz@^2.6.0:
+  version "2.7.0"
+  resolved "https://registry.yarnpkg.com/mz/-/mz-2.7.0.tgz#95008057a56cafadc2bc63dde7f9ff6955948e32"
+  integrity sha512-z81GNO7nnYMEhrGh9LeymoE4+Yr0Wn5McHIZMK5cfQCl+NDX08sCZgUc9/6MHni9IWuFLm1Z3HTCXu2z9fN62Q==
+  dependencies:
+    any-promise "^1.0.0"
+    object-assign "^4.0.1"
+    thenify-all "^1.0.0"
+
 nan@^2.9.2:
   version "2.10.0"
   resolved "https://registry.yarnpkg.com/nan/-/nan-2.10.0.tgz#96d0cd610ebd58d4b4de9cc0c6828cda99c7548f"
@@ -2383,7 +2445,7 @@ oauth-sign@~0.8.2:
   version "0.8.2"
   resolved "https://registry.yarnpkg.com/oauth-sign/-/oauth-sign-0.8.2.tgz#46a6ab7f0aead8deae9ec0565780b7d4efeb9d43"
 
-object-assign@^4.1.0:
+object-assign@^4.0.1, object-assign@^4.1.0:
   version "4.1.1"
   resolved "https://registry.yarnpkg.com/object-assign/-/object-assign-4.1.1.tgz#2109adc7965887cfc05cbbd442cac8bfbb360863"
 
@@ -2518,6 +2580,11 @@ parse5@4.0.0:
   version "4.0.0"
   resolved "https://registry.yarnpkg.com/parse5/-/parse5-4.0.0.tgz#6d78656e3da8d78b4ec0b906f7c08ef1dfe3f608"
 
+parsimmon@^1.2.0:
+  version "1.12.0"
+  resolved "https://registry.yarnpkg.com/parsimmon/-/parsimmon-1.12.0.tgz#886a442fb30b5fc3c8e7c4994050f5cdcfe0ea90"
+  integrity sha512-uC/BjuSfb4jfaWajKCp1mVncXXq+V1twbcYChbTxN3GM7fn+8XoHwUdvUz+PTaFtDSCRQxU8+Rnh+iMhAkVwdw==
+
 pascalcase@^0.1.1:
   version "0.1.1"
   resolved "https://registry.yarnpkg.com/pascalcase/-/pascalcase-0.1.1.tgz#b363e55e8006ca6fe21784d2db22bd15d7917f14"
@@ -3158,7 +3225,7 @@ strip-eof@^1.0.0:
   version "1.0.0"
   resolved "https://registry.yarnpkg.com/strip-eof/-/strip-eof-1.0.0.tgz#bb43ff5598a6eb05d89b59fcd129c983313606bf"
 
-strip-json-comments@~2.0.1:
+strip-json-comments@^2.0.1, strip-json-comments@~2.0.1:
   version "2.0.1"
   resolved "https://registry.yarnpkg.com/strip-json-comments/-/strip-json-comments-2.0.1.tgz#3c531942e908c2697c0ec344858c286c7ca0a60a"
 
@@ -3210,6 +3277,20 @@ test-exclude@^4.2.1:
     read-pkg-up "^1.0.1"
     require-main-filename "^1.0.1"
 
+thenify-all@^1.0.0, thenify-all@^1.6.0:
+  version "1.6.0"
+  resolved "https://registry.yarnpkg.com/thenify-all/-/thenify-all-1.6.0.tgz#1a1918d402d8fc3f98fbf234db0bcc8cc10e9726"
+  integrity sha1-GhkY1ALY/D+Y+/I02wvMjMEOlyY=
+  dependencies:
+    thenify ">= 3.1.0 < 4"
+
+"thenify@>= 3.1.0 < 4":
+  version "3.3.0"
+  resolved "https://registry.yarnpkg.com/thenify/-/thenify-3.3.0.tgz#e69e38a1babe969b0108207978b9f62b88604839"
+  integrity sha1-5p44obq+lpsBCCB5eLn2K4hgSDk=
+  dependencies:
+    any-promise "^1.0.0"
+
 throat@^4.0.0:
   version "4.1.0"
   resolved "https://registry.yarnpkg.com/throat/-/throat-4.1.0.tgz#89037cbc92c56ab18926e6ba4cbb200e15672a6a"
@@ -3343,6 +3424,24 @@ tslint@^5.10.0:
     tslib "^1.8.0"
     tsutils "^2.12.1"
 
+tslint@^5.9.1:
+  version "5.11.0"
+  resolved "https://registry.yarnpkg.com/tslint/-/tslint-5.11.0.tgz#98f30c02eae3cde7006201e4c33cb08b48581eed"
+  integrity sha1-mPMMAurjzecAYgHkwzywi0hYHu0=
+  dependencies:
+    babel-code-frame "^6.22.0"
+    builtin-modules "^1.1.1"
+    chalk "^2.3.0"
+    commander "^2.12.1"
+    diff "^3.2.0"
+    glob "^7.1.1"
+    js-yaml "^3.7.0"
+    minimatch "^3.0.4"
+    resolve "^1.3.2"
+    semver "^5.3.0"
+    tslib "^1.8.0"
+    tsutils "^2.27.2"
+
 tsutils@^1.4.0:
   version "1.9.1"
   resolved "https://registry.yarnpkg.com/tsutils/-/tsutils-1.9.1.tgz#b9f9ab44e55af9681831d5f28d0aeeaf5c750cb0"
@@ -3353,6 +3452,13 @@ tsutils@^2.12.1:
   dependencies:
     tslib "^1.8.1"
 
+tsutils@^2.27.2:
+  version "2.29.0"
+  resolved "https://registry.yarnpkg.com/tsutils/-/tsutils-2.29.0.tgz#32b488501467acbedd4b85498673a0812aca0b99"
+  integrity sha512-g5JVHCIJwzfISaXpXE1qvNalca5Jwob6FjI4AoPlqMusJ6ftFE7IkkFoMhVLRgK+4Kx3gkzb8UZK5t5yTTvEmA==
+  dependencies:
+    tslib "^1.8.1"
+
 tunnel-agent@^0.6.0:
   version "0.6.0"
   resolved "https://registry.yarnpkg.com/tunnel-agent/-/tunnel-agent-0.6.0.tgz#27a5dea06b36b04a0a9966774b290868f0fc40fd"
@@ -3369,9 +3475,15 @@ type-check@~0.3.2:
   dependencies:
     prelude-ls "~1.1.2"
 
+typescript@next:
+  version "3.2.0-dev.20181116"
+  resolved "https://registry.yarnpkg.com/typescript/-/typescript-3.2.0-dev.20181116.tgz#0a405b3385d6f180df78bf557167c0a608b5a501"
+  integrity sha512-+UUHAGhfccJe1ZnHbqp0uixDjT/yMguznOvF1p+16ytQPJaFo2MfIt6on4PZlgl7VhdxtENSfzl44xxjWsfj8Q==
+
 typescript@~2.9.1:
   version "2.9.2"
   resolved "https://registry.yarnpkg.com/typescript/-/typescript-2.9.2.tgz#1cbf61d05d6b96269244eb6a3bce4bd914e0f00c"
+  integrity sha512-Gr4p6nFNaoufRIY4NMdpQRNmgxVIGMs4Fcu/ujdYk3nAZqk7supzBE9idmvfZIlH/Cuj//dvi+019qEue9lV0w==
 
 uglify-js@^2.6:
   version "2.8.29"