exponent and radical rules (6.1, 6.2) day 1 · exponents x0=1 division xa xb =xa ... 4 reduce any...
TRANSCRIPT
DAY 1
Exponent and Radical Rules (6.1, 6.2)
Name: ___________________________________________________ Block: ______________
Topic Definition/Rule Example(s)
Multiplication xa ⋅ xb = xa+b
Power to a Power xa( )b = xab
Power of a Product
ab( )n =anbn
Zero
Exponents x0 =1
Division
xa
xb = xa−b
Power of a Quotient
xy
⎛
⎝⎜
⎞
⎠⎟
n= xn
yn
Simplifying
1.
2.
3.
Simplifying Exponents
Step Method Example
1 Label all unlabeled exponents “1”
2 Take the reciprocal of the fraction and make the outside exponent positive.
3 Get rid of any inside parentheses.
4 Reduce any fractional coefficients.
5 Move all negatives either up or down.
Make the exponents positive.
6 Combine all like bases.
7 Distribute the power to all exponents.
Use properties of exponents to simplify the following expressions.
f.
g. h. 121/8 125/6 =
i. (51/3 x1/4)3 = j. (26 46)-1/6 =
k. = l.
RATIONAL EXPONENTS
QUESTION: What is the square root of a number? Determine what number fits into the . a. 5 i 5 = 5 is the _____________ of 25 b. 10 i 10 = 10 is the _____________ of 100 c. x i x = _____ is the square root of ______ d. x 3 i x 3 = _____ is the square root of ______ e. x 9 i x 9 = _____ is the square root of ______ QUESTION: What does the square root of x mean?
x i x = x1 is the square root of x. RULE: __________________________
FRACTIONAL EXPONENT RULE:
For any real number a and integers n and m: _____________________________
Examples:
a. 161/2 = = 4 b. 271/3 = = 3
c. (-8)1/3 = = -2 d. (16)1/4 = = 2
RATIONAL EXPONENTS
Exponent (numerator)
x1/2
Base (x) Root (denominator)
RADICALS
Index
Radicand
ExponentialNotation
RadicalNotation
x1/2
x2/3
x3/4
am/n
a-m/n
RULE:
EXAMPLES:
Evaluate each of the following without the use of a calculator!
1. 2. 3. 4.
5. 6. 7. 8.
9. 10. 11. 12.
RULE:
EXAMPLES:
Evaluate each of the following without the use of a calculator!
1. 2. 3. 4.
5. 6. 7. 8.
9. 10. 11. 12.
A negative exponent was slipped into that last problem! How did you deal with it?
RULE:
EXAMPLES:
Evaluate each of the following without the use of a calculator!
1. 2. 3. 4.
5. 6. 7. 8.
9. 10. 11. 12.
Mad Math Minute!
Name: __________________________________ Date: __________
1. x2
3 = ______ 2.
x2( )3 = ______ 3.
x4( )7 = ______
4.
x3( )4 = _____ 5. x13 = ______ 6. 100
12 = ______
7. y13 = ______ 8.
x 34⎛
⎝⎜⎞⎠⎟
= ______ 9. x3
2 = ______
10. 4912 = ______ 11. x
15 = ______ 12.
x 4⎛
⎝⎜⎞⎠⎟
= ______
13. x12 = ______ 14. 16
12 = ____ 15.
x 35⎛
⎝⎜⎞⎠⎟
= ______
16. x51 = ______ 17.
x15⎛
⎝⎞⎠
3 = ______ 18. 4
32 = ______
DAY 2
RADICALS
Warm Up Simplify the following square root and cube root expressions
1.
2.
3.
4.
EXAMPLE ONE Simplifying square roots with variables
a) b)
EXAMPLE TWO Rationalizing the denominator
a)
5
63 b)
7
1+ 2 5
EXAMPLE THREE Multiplying Radical Expressions
c) d)
EXAMPLE FOUR Adding and Subtracting Radical Expressions
a)
b)
c)
PRACTICE
1. 2. 3. x11
4. 5.
6.
Simplify using the exponent rules. (No decimals, keep as fractions)
1.
2. 3.
4.
5. (a3b‐6)(a2b0)6.
7. 8. 9.
1. 5. 6.
7. 9.
10.
12. 243 − 33
15. 6 323 − 5 43 4.
2. 13.
53 + 7
14.
21− 4 3
EXPONENT PROPERTIES
EXAMPLE FOUR Re-write the radical expression in exponential form.
a) b) c) d)
EXAMPLE FIVE Simplify the expression without using a calculator.
a)
b)
c)
d)