Exponent Properties
Exponent Properties
[pic] (n times).
Example: [pic]
1. Zero Exponent: [pic]
ANY number raised to the zero power is equal to “1”.
Example: [pic]
Example: [pic]
2. The “One” Exponent: [pic]
ANY number raised to the first power is equal to itself.
Example: [pic]
Example: [pic]
3. Negative Exponent: [pic] or [pic]
We don’t like negative exponents, we want positive exponents! To make a negative exponent positive, take the reciprocal. A negative exponent in the denominator (bottom) moves to the numerator (top) and becomes positive and a negative exponent in the numerator (top) moves to the denominator (bottom) and becomes positive. You may want to think of it this way, make an exponent positive by “switching floors”!
Example: [pic]
Example: [pic]
Example: [pic]
4. Product of Powers: [pic]
When multiplying powers with the same base, add the exponents and keep the common base.
Example: [pic]
Example: [pic]
5. Quotient of Powers: [pic]
When dividing powers with the same base, subtract the exponents and keep the common base.
Example: [pic]
Example: [pic]
6. Power of a Power: [pic]
The key is PARENTHESES!!! To raise a power to a power(exponent to an exponent), keep the base and multiply the exponents.
Example: [pic]
Example: [pic]
7.
8. Power of a Product: [pic]
The key is PARENTHESES!!! Distribute the exponent to each base: multiply the exponents.
Example: [pic]
9. Power of a Quotient: [pic]
The key is PARENTHESES!!! To raise a power to a power(exponent to an exponent), keep the base and multiply the exponents.
Example: [pic]
10. Rational Exponents:
Example: [pic]
Example: [pic]
11.
12. When the base is negative and the exponent is…
o Odd – the base remains negative
o Even – the base becomes positive
Example (Odd):[pic]
Example (Even): [pic]
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