Download - Radicals Rational Exponents
RadicalsRational Exponents
Target Goals: Write expressions with rational exponents in simplest radical form and vice versa;
Evaluate expressions in either exponential or radical form
Opener – Simplify each of the following using your exponent rules from the last chapter.
2 3x x 5x3 7x x 4x
6
2
xx
4x
2
9
xx
7x 7
1x
1 25 5x x
35x
1 16 3x x
1 26 6x x
36x
12x
58
14
x
x
5 18 4x
5 28 8x
38x
Opener – Simplify each of the following using your exponent rules from the last chapter.
42x 8x
23x 6x
312x
32x
13 64x
324x
18x
6
1x
Rational exponents are FRACTION EXPONENTS.
RATIONAL EXPONENTS:
an a nb b
Write the following in radical form.16Ex 1) x 6 x
74Ex 2) d 74 d
Write the following in exponential form.
4Ex 3) z14z 3 5Ex 4) d
53d
An expression with rational exponents is simplified when all of the following conditions are met: It has no negative exponents. It has no exponents that are not positive
integers in the denominator (i.e., no fraction exponents in the denominator).
It is not a complex fraction (i.e., fractions within fractions).
The index of any remaining radical is the least number possible (i.e., the fraction exponent is as simplified as possible).
Evaluate each expression/Simplify:14Ex 5) 81
14
1
81
4
181
4
13 3 3 3
13
14
1
81
1
4 4
1
3 14
4
1
3
13
1
4 43
1313
Evaluate each expression/Simplify:15Ex 6) 3125
15
1
3125
5
13125
5
15 5 5 5 5
15
1
5 5
1
5
15
1
5 55
15 15
Evaluate each expression/Simplify:23Ex 7) 216
23 36 26 36
3
8 82 32 838Ex 8) 256
1 94 4Ex 9) p p
104p
52p
Evaluate each expression/Simplify:45Ex 10) r
45
1
r
15
15
r
r
15rr
5 4
1
r
5
5
rr
5
5 5
r
r
5 rr
15rr
Simplify each expression:4 27Ex 11)
3
14
12
27
3
1
3 4
12
3
3
34
12
3
3
3 14 23
3 24 43
143 4 3
3 6Ex 12) 64z1 63 364 z
613 334 z 24z
Simplify: 12
12
2Ex 13) 2
y
y
22
yy
22
yy
2 2 42 2 4
y y yy y y
4 44
y yy
124 44
y yy
Multiply by the conjugate!!