Exponent Properties
1. Product of like bases: ![](./articles_imgs/422/pic1.gif)
To multiply powers with the same base, add the exponents and
keep the common base.
Example: ![](./articles_imgs/422/pic2.gif)
2. Quotient of like bases: ![](./articles_imgs/422/pic3.gif)
To divide powers with the same base, subtract the exponents
and keep the common base.
Example: ![](./articles_imgs/422/pic4.gif)
3. Power to a power: ![](./articles_imgs/422/pic5.gif)
To raise a power to a power, keep the base and multiply the
exponents.
Example: ![](./articles_imgs/422/pic6.gif)
4. Product to a power: ![](./articles_imgs/422/pic7.gif)
To raise a product to a power, raise each factor to the power.
Example: ![](./articles_imgs/422/pic8.gif)
5. Quotient to a power ![](./articles_imgs/422/pic9.gif)
To raise a quotient to a power, raise the numerator and the
denominator to the power.
Example: ![](./articles_imgs/422/pic10.gif)
6. Zero Exponent:![](./articles_imgs/422/pic11.gif)
Any number raised to the zero power is equal to 1.
Example: ![](./articles_imgs/422/pic12.gif)
7. Negative exponent: ![](./articles_imgs/422/pic13.gif)
Negative exponents indicate reciprocation, with the exponent
of the reciprocal becoming positive. You may want to think of it
this way: unhappy (negative) exponents will become happy
(positive) by having the base/exponent pair switch
floors!
Example: ![](./articles_imgs/422/pic14.gif)
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