# Basic laws of calculating exponents

Get to know the math exponents, their basic properties and review some examples of using that.

First of all, there is a table of basic exponents. With these properties you can solve many tasks included rational exponents.

\begin{array}{|c|c|} \hline a^n\cdot a^m=a^{n+m} & a^n:a^m=a^{n-m} \\\hline a^0=1 & (a^n)^m=a^{n\cdot m} \\\hline (a\cdot b)^n=a^n\cdot b^n & \left(\frac{a}{b}\right)^n=\frac{a^n}{b^n} \\\hline a^{-n}=\frac{1}{a^n} & \left(\frac{a}{b}\right)^{-n}=\left(\frac{b}{a}\right)^n \\\hline \end{array}## Solved examples

Let's solve some example tasks to see how easy to find all values of these terms.

**Example No. 1.** Simplify this expression and write answer without fraction: $\displaystyle\frac{105(x^{-2}y^{-4})^{-2}}{3(x^3)^{-2}(y^7)^{-3}}$

$$\frac{105(x^{-2}y^{-4})^{-2}}{3(x^3)^{-2}(y^7)^{-3}}=\frac{105x^{4}y^{8}}{3x^{-6}y^{-21}}=35x^{10}y^{29}$$

2020-11-29

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