# Powers and Roots Rules

Here are all the formulas you need in order to succeed in the course. Mastering these formulas will save you a lot of time in solving exercises and will help you avoid unnecessary calculation errors 🙂

## 1. Multiplication:

$${(xy)}^n=x^n y^n$$

$$x^n x^m=x^{n+m}$$

## 2. Division:

$${(\frac{x}{y})}^n=\frac{x^n}{y^n}$$

$$\frac{x^n}{x^m}=x^{n-m}$$

## 3. Powers:

$${(x^n)}^m=x^{nm}$$

$$x^{-n}=\frac{1}{x^n}$$

$$x^0=1$$

## 4. Roots:

$$x^{\frac{n}{m}}=\sqrt[m]{x^n}$$

$$x^{\frac{n}{m}}=\sqrt[m]{x^n}$$

$$\sqrt[n]{xy}=\sqrt[n]{x}\sqrt[n]{y}$$

$$\sqrt[n]{\frac{x}{y}}=\frac{\sqrt[n]{x}}{\sqrt[n]{y}}$$

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