4.4 fractional exponents and...
TRANSCRIPT
4.4 Fractional Exponents and Radicals.notebook
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Activate Prior Learning:
Exponent Laws
Entrance Slip
Write as a single power.
a)
b)
c)
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What did you notice about the numbers and powers in the first column of the table?
They are consecutive square numbers.
What did you notice about the powers in the second column?
Each has an exponent of 1/2 and has the same value as the square root of the number in the first column.
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What did you notice about the numbers and powers in the first column of the table?
They are consecutive cube numbers.
What did you notice about the powers in the second column?
Each has an exponent of 1/3 and has the same value as the cube root of the number in the first column.
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1n
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In grade 9, you learned that for powers with integral bases and whole number exponents:am . an = am + n
(To multiply powers with the same base, add the exponents)
52 . 53 = 52+3 = 55
We can extend this law to powers with fractional exponents with numerator 1:
Powers with Rational Exponents with Numerator 1
When n is a natural number and x is a rational number,
The denominator becomes the index and the base becomes the radicand.
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Example 1: Evaluating Powers of the Form
Solution:
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You try...
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In grade 9, you also learned:
(am)n = amn
When a power is raised to another power, multiply the two exponents together.(52)3 = 52 x 3 = 56
We can extend this exponent law so that it applies when m and n are rational numbers.
Powers with Rational Exponents
When m and n are natural numbers, and x is a rational number,
and
The numerator of the exponent stays as an exponent and the denominator becomes the index.
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Example 2: Rewriting Powers in Radical and Exponent Form
Solution:
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You try...
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Page 227 #7 and 10
Practice leads to Proficiency
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Example 3: Evaluating Powers with Rational Exponents and Rational Bases
Solution:
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You try...
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P. 227 # 3,5,6,8,11,16a
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Entrance Slip
1. Write each of the following as a radical:a) 8(1/6) b) 3(8/2)
2. Write each of the following as a power:a) 10 b) 9
3. Simplify the following:((a2b3)3)(ab)
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Example 4: Applying Rational Exponents
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You try...
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p.228 #17, 18, 19, 20 a, 20 b
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