Basic Rules of Exponents

Multiplying Powers with the Same Base

$a^{n} \times a^{m}=a^{n+m}$

$a n$ mean that you have $a$ a factor of $n$ times. If you add $m$ more factors of $a$ then you have $n + m$ factors of $a$ .

Dividing Powers with the Same Base

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

In the same way that $a^{n} \times a^{m}=a^{n+m}$ because you are adding on factors of $a$ , dividing is taking away factors of $a$ .

Raising a Power to a Power

$a^{n^{m}}=a^{n \times m}$

If you think about an exponent as telling your that you have so many factors of the base, then $a^{n^{m}}$ means that you have $m$ factors of $a n$ . So you have m groups of $a n$ and each one of those has $n$ groups of $a$ . So you have $m$ groups of $n$ groups of $a$ . So you have $n \times m$ groups of a, or $a^{n^{m}}$

Any Nonzero number Raised to the Zero Power Is One

$a \ne 0 \implies a^{0} = 1$

Extracted from http://en.wikibooks.org/wiki/Algebra_I_in_Simple_English. Reproduced under the GNU Free Documentation License

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