10/14/2013
Quiz 1 – Exponents/Radicals
Rewriting
• When rewriting a radical in exponential form:
– The root becomes the denominator
– The exponent becomes the numerator
– Remember, a
is really a
2
!
• When rewriting a exponential in radical form:
– The denominator becomes the root
– The numerator becomes the exponent
Rewriting
Examples:
Rewrite in exponential form
𝑥 3 becomes 𝑥 3/2
Practice:
Rewrite in exponential form
3
𝑥
( 5𝑥)4
Rewrite in radical form
(3𝑦)5/3 becomes
3
(3𝑦)5
Rewrite in radical form
𝑥 1/2
(6𝑚)2/5
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10/14/2013
Evaluating
When given a number to a fractional exponent:
Examples:
813/2
84/3
First rewrite in radical form with the root on the
inside
3
2
( 81)3
( 8)4
Then find the root and then perform the
exponent
(9)3 = 729
(2)4 = 16
Simplifying Radicals
• For square roots:
Examples:
54
40𝑥 5
Break the inside into perfect squares
9∗ 6
4 ∗ 10 ∗ 𝑥 2 ∗ 𝑥 2 ∗ 𝑥
Simplify the square roots if possible:
3 6
2 10 ∗ 𝑥 ∗ 𝑥 ∗ 𝑥
Practice:
60𝑥 6
75
Simplifying Radicals
• For cube roots:
Examples:
3
3
𝑥6
𝑥10
Break apart the inside into perfect cubes
3
3
𝑥3 ∗ 𝑥3
Simplify the cube roots if possible
𝑥∗𝑥
3
3
3
𝑥3 ∗ 𝑥3 ∗ 𝑥3 ∗ 3 𝑥
𝑥∗𝑥∗𝑥∗ 3 𝑥
Practice:
3
𝑦7
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Properties of Exponents
• 𝑎𝑚 ∗ 𝑎𝑛 = 𝑎𝑚+𝑛
•
𝑏𝑚
= 𝑏 𝑚−𝑛
𝑏𝑛
𝑚 𝑛
𝑚∗𝑛
• (𝑏 ) = 𝑏
• (𝑎𝑏)𝑚 = 𝑎𝑚 𝑏 𝑚
1
• 𝑏 −𝑚 = 𝑏𝑚
•
1
𝑏 −𝑛
= 𝑏𝑛
Properties of Exponents
(–2a3b)–3
3z7(–4z2)
3  (–4)  z7  z2
–12z7 + 2
–12z9
Practice:
(yz3 – 5)3 = (yz–2)3
y3(z–2)3
y3z(–2)(3)
8y6(–6y3)
3