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
Product of Powers Property a m x a n = a m+n Example: 5 4 x 5 8 =5 4+8 =5 12 Note: Remember SAME bases --> ADD the exponents
Power of a Power Property (a m ) n =a mn Basically just multiply the exponents Examples: (4 3 ) 2 = 4 3x2 = 4 6
Power of A Product Property (ab) m = a m b m (3n) 4 = 3 4 n 4 Remember this is not true for (3+n) 4 : you cannot distribute the exponent in this case
Negative Exponent Property a -n = 1/a n or 1/a -n = a n Example: 8 -2 = 1/8 2 = 1/64 Note: Negative exponents indicate reciprocation, with the exponent of the reciprocal becoming positive.
Zero Exponent Property a 0 = 1 Examples: 6 0 =1 (8x 4 ) 0 =1 Remember that any number raised to the zero power is equal to “1”.
Quotient of Powers Property (a/b) n = a n /b n To raise a quotient to a power, raise the numerator and the denominator to the power. Example: ( a 3 / b 2 ) 4 = ( a 12 / b 8 )
Power of A Quotient Property a b /a c = a b-c Example: 9 5 /9 2 = 9 3 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.
I hope these slides helped you to understand the properties of exponents! :)