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Answer:
Laws of Radical Expressions
The laws for radicals are derived directly from the laws for exponents by using the definition a m n = a m n . The laws are designed to make simplification much easier.
LAW EXAMPLESimplified Answer
( a n ) n =a ( 8 3 ) 3 = (2) 3 =8
a n = a 1 n (a) 5 = 5 1 2
(b) 17 3 = 17 1 3
ab n = a n • b n (a) 4•3 = 4 • 3 = 2 3
Write the radicand as a product (b) 16 3 = 8•2 3 = 8 3 • 2 3 = 22 3
a b n = a n b n (a) 16 81 4 = 16 4 81 4= 2 3
(b) 3 16 = 3 16 3 4
a m n = ( a n ) m 27 2 3 = ( 27 3 ) 2= (3)2 = 9
a n m = a mn 256 3 2 = 256 2⋅3 = 256 6 = 2
It is important to reduce a radical to its simplest form. Using the laws of radicals for multiplication, division, raising a power to a power, and taking the radical of a radical makes the simplification process for radicals much easier.