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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