DAY 1 Exponent and Radical Rules (6.1, 6.2) Name: ___________________________________________________ Block: ______________ Topic Definition/Rule Example(s) Multiplication x a ⋅ x b = x a +b Power to a Power x a ( ) b = x ab Power of a Product ab ( ) n = a n b n Zero Exponents x 0 = 1 Division x a x b = x a −b Power of a Quotient x y ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ n = x n y n Simplifying 1. 2. 3.
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Exponent and Radical Rules (6.1, 6.2) DAY 1 · Exponents x0=1 Division xa xb =xa ... 4 Reduce any fractional coefficients. 5 Move all negatives either up or down. Make the exponents
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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!