Properties Of Exponents

1. Properties Of Exponents Haley Dowdie, Ariana Langston, & Lynn Nguyen

2. What are the Properties? Product of Powers Property Power of A Power Property Power of A Product Property Negative Exponent Property Zero Exponent Property Quotient of Powers Property Power of A Quotient Property Don't worry too much about the names! What's important is understanding each concept

3. Product of Powers Property • am x an = am+n • Example: 54x 58=54+8 =512 • Note: • Remember SAME bases --> ADD the exponents

4. Power of a Power Property (am)n =amn Basically just multiply the exponents Examples: (43)2= 43x2= 46

5. Power of A Product Property (ab)m= ambm (3n)4= 34n4 Remember this is not true for (3+n)4: you cannot distribute the exponent in this case

6. Negative Exponent Property a-n = 1/an or 1/a-n = an Example: 8-2 = 1/82 = 1/64 Note: Negative exponents indicate reciprocation, with the exponent of the reciprocal becoming positive.

7. Zero Exponent Property a0 = 1 Examples: 60 =1 (8x4)0 =1 Remember that any number raised to the zero power is equal to “1”.

8. Quotient of Powers Property (a/b)n = an/bn To raise a quotient to a power, raise the numerator and the denominator to the power. Example: (a3/b2)4= (a12/b8)

9. Power of A Quotient Property ab/ac = ab-c Example: 95/92 = 93 When you divide two powers with the same base, you subtract the exponents. For all real numbers a,b, and c, when a doesn't equal to 0.

10. I hope these slides helped you to understand the properties of exponents! :)