math 20 dec exam
product law
Am x An = Am+n
quotient law
Am ÷ An = Am-n
power rule
(Am)n = Amn
distrubitivity over products
(AB)m = AmBm
distributivity over quotients
(A/B)m = Am/Bm; B cant be zero
power of zero
A0 = 1; A cant be zero
nth root
The "nth Root" used n times in a multiplication gives the original value.
multiplication property of a radical
n√ab = n√a x n√b.
example: √24 = √4x6 = √4 x √6 = 2√6
entire radical
an expression of An√x where a must be 1 or -1. e.g. 3√17 is an entire radical but 2n√2 is not
mixed radical
an expression of An√x where a cannot be 1 or -1. e.g. 5n√9 is an entire radicalm
mixed to entire radical
1. identify the mixed radical
2. raise the coefficient to the nth root
3. multiply the og radicand by the result of step 2.
4. write the result inside the radical symbol
entire to mixed radical
1. identify the entire radical
2. find the largest perfect power of the radicand
3. rewrite as a product of the two radicals in step 2
4. simplify the perfect power radical
5. put the result from step 4 outside the radical sign and keep the radicand inside.
when is a radical simplified
if the radicand doesnt contain any factors that are perfect powers
rational exponents
n√x = x1/n. ex) 3√2 = 2 1/3