5.1 Properties of Exponents
Product Property: am an = am+n
Power-to-Power: (am)n = amn
Product-to-Power: (ab)m = ambm
Negative Exponent: a-m = 1 , a≠0. and
am
1 = am
a-m
Zero Exponent: a0=1, a≠0
Quotient Rule: am = am-n , a≠0.
an
Quotient to Power: a
b
= am
bm
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Examples: Evaluate the expressions.
1.) 22 25
2.) (33)2
3.) 5
4
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1
4.) 5-6 54
5.) 5
3
6.) (-2)0(-2)3(-2)2
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Examples: Simplify the expressions.
1.) (2xy3)3
2.) (3p3q2)-1
3.) (w3x-2)(w-5x4)
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2
4.) 4r4s5
24r4s-5
5.) x4y-2 y3
4y-5 x-4
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Example: Write an expression that makes
the statement true.
3x3y2 = 12x2y5
?
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3
Examples: Write an expression for the
figure's area or volume in terms of x.
1.) A = √3 s2
4
x
3
2.) V = lwh
x
2x
5x
3
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Scientific Notation: a x 10n, where 1≤ IaI <10.
Examples: Write the answer in scientific notation.
1.) (1.2 x 10-3)(6.7 x 10-7)
2.) (7.2 x 109)(9.4 x 108)
3.) (3.1 x 10-3)3
4.) (6.5 x 109)(3.5 x 10-5)
2.5 x 106
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4