section 1.2 exponents & radicals objectives: to review exponent rules to review radicals to...
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Section 1.2 Exponents & Radicals
Objectives:•To review exponent rules•To review radicals•To review rational exponents
Integer Exponents
factorsn an = a · a · · · · · a
The number a is called the base and n is called the exponent.
Zero & Negative Exponents
If a ≠ 0 is any real number and n is a positive integer, then
a0 = 1 and a–n = 1na
nth Roots
If 24 = 16, then it follows that .
4 16 2
If n is any positive integer, then the principal nth root of a is defined as follows:
If n is even, we must have a ≥ 0 and b ≥ 0.
means nn a b b a
Properties of nth Roots
Property Example1.
2.
3.
n n nab a b 3 8 27
n
nn
a a
b b 4
16
81
3 38 27 2 3 6
4
4
16 2
381
m n mna a3 729 6 729 3
Rational Exponents
For example,
and,
For example,
1/ n na a
31/ 3x x
/ /( ) or equivalentlym n m m n mnna a a a
23 32 / 3 2x x or x
Class Work
11.
12.
13.
14.
1/ 3 7 / 3a a
2 / 5 7 / 5
3 / 5
a a
a
3 / 23 42a b
33 / 4 4
1/ 3 1/ 2
2x y
y x
8 / 3a
9 / 5
6 53 / 5
aa
a3 2 9 2 62 a b
9 4
4 1 2 11 4 388
xy x x y
y
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