Download section p2 exponents and radicals

Notes Section P2: Exponents and Radicals
This lesson will cover the competencies of the real number system and arithmetic with
rational expressions.
Summarize the following rules for Properties of Exponents:
Let a and b be real numbers and let m and n be integers.
1. am · an =
2. (am)n =
3. (ab)m =
4. a-n =
5. a0 =
6. am =
an
7. (a )m =
b
Ex 1: Evaluate each expression:
a. (-3)(-3)5
b. [(-2)3]3
c. (32xy)4
d. 4-3· 43
Ex 2: Simplify and write each expression with positive exponents only:
a. r-1· r4
r6
b. 3 m5n · 4m-2n-1
m2n9
9mn2
Ex 3: Simplify and write each expression with positive exponents only:
a. 5d-3
b.
𝑝−1
𝑞−5
c. -20a-2b4
5 a-3b-1
Scientific Notation: Used to help compute with either very ________________ or
very___________________ numbers.
How do we change a number to scientific notation? What should it look like?
Ex 4: Change the following to scientific notation:
a. 326,000,000,000
b. 0.000000000000985
Ex 5: Change to standard form:
a. 1.345 x 105
b. 4.56 x 10-7
Ex 6: Calculate (3 x 103)(2.5 x 105)
Radicals
Properties: Use pg 16 in your book to fill in the 6 properties for radicals:
1.
2.
3.
4.
5.
6.
Ex 7: Evaluate the following expressions:
a. √36
b. - √36
3
c. √
d.
e.
Ex 8:
a.
b.
c.
d.
125
64
5
4
√-32
√-81
Simplify each expression:
√8 ∙ √2
(3√5)3
3
√x3
6
√y6
An expression involving radicals is in simplest form when the following conditions are satisfied:
1. All possible factors are removed from the radical.
2. All fractions have radical-free denominators.
3. The index of the radical is reduced.
Ex 9: Simplify the following:
a. 4√48
b. √75x3
c.
4
√(5x4)
Ex 10: Simplify:
a. 3√24
b.
3
√24a4
c.
3
√-40x6
How can you add or subtract radicals?
Ex 11: Combine:
a. 2√48 - 3√27
b.
3
√16 - 3√54x4
Rationalizing the denominator:
Ex 12: Rationalize the denominator of each expression:
a.
5
b. 2
3
2√3
√5
Ex 13: Rationalize
2
3 + √7
Rational exponents:
Ex 14: Change the following from radical form to rational exponent form:
a. √3
b. 2x 4√x3
Ex 15: Change to radical form:
a. (x2 + y2)3/2
b. 2y3/4z1/4
Ex 16: Simplify:
a. (-32)-4/5
b.
9
√a3
c.
3
√ √125
d. (2x – 1)4/3(2x – 1)-1/3
e.
x–1
(x – 1)-1/2