1-5
Properties of Exponents
Zero Exponent Property: Any nonzero value raised to
the zero power equals 1.
1000 = 1
a0 = 1
Negative Exponent Property: Any nonzero base raised
to a negative exponent is equal to the reciprocal of the
based raised to the positive exponent.
7−2
=
1 2
7
Holt Algebra 2
=
1
72
𝑎−𝑛
=
1 𝑛
𝑎
=
1
𝑎𝑛
1-5
Properties of Exponents
Example 2A: Simplifying Expressions with Negative
Exponents
Simplify the expression.
3–2
The reciprocal of
Holt Algebra 2
.
1-5
Properties of Exponents
Example 2B: Simplifying Expressions with Negative
Exponents
Simplify the expression.
The reciprocal of
Holt Algebra 2
.
1-5
Properties of Exponents
Check It Out! Example 2a
Simplify the expression.
𝑥 −3
𝑦2
1
1
× 2
3
𝑥
𝑦
1
𝑥3𝑦2
Holt Algebra 2
The reciprocal of x-3 is
1
.
𝑥3
1-5
Properties of Exponents
Product of Powers Property: To multiply powers with
the same base, add the exponents.
43∙42 = 43+2 = 45
am + an = am+n
Quotient of Powers Property: To divide powers with the
same base, subtract the exponents.
37
32
=
37−2
Holt Algebra 2
=
35
𝑎𝑚
𝑎𝑛
= 𝑎𝑚−𝑛
1-5
Properties of Exponents
Power to a Power Property: To raise one power to
another power, multiply the exponents.
(43)2= 43∙2 = 46
(am)n= am∙n
Power of Product Property: To find the power of a
product, apply the exponents to each factor.
(3∙4)2= 32∙42
(ab)n= an∙bn
Holt Algebra 2
1-5
Properties of Exponents
Power of a Quotient Property: To find the power of a
quotient, apply the exponent to the numerator and
denominator.
3 2
5
=
32
52
Holt Algebra 2
𝑎 𝑛
𝑏
=
𝑎𝑛
𝑏𝑛
1-5
Properties of Exponents
Example 3A: Using Properties of Exponents to
Simplify Expressions
Simplify the expression. Assume all variables
are nonzero.
3z7(–4z2)
3  (–4)  z7  z2
–12z7 + 2
–12z9
Holt Algebra 2
Product of Powers
Simplify.
1-5
Properties of Exponents
Example 3B: Using Properties of Exponents to
Simplify Expressions
Simplify the expression. Assume all variables
are nonzero.
(yz3 – 5)3 = (yz–2)3
Quotient of Powers
y3(z–2)3
Power of a Product
y3z(–2)(3)
Power of a Product
Negative of Exponent Property
Holt Algebra 2
1-5
Properties of Exponents
Check It Out! Example 3a
Simplify the expression. Assume all variables
are nonzero.
(5x6)3
53(x6)3
Power of a Product
125x(6)(3)
Power of a Power
125x18
Holt Algebra 2
1-5
Properties of Exponents
Check It Out! Example 3b
Simplify the expression. Assume all variables
are nonzero.
(–2a3b)–3
Negative Exponent Property
Power of a Power
Holt Algebra 2
1-5
Properties of Exponents
Scientific notation is a method of writing
numbers by using powers of 10. In scientific
notation, a number takes a form m  10n, where
1 ≤ m <10 and n is an integer.
Ex)
3.0  10–11
Holt Algebra 2
Divide 4.5 by 1.5 and subtract
exponents: –5 – 6 = –11.
1-5
Properties of Exponents
Example 4B: Simplifying Expressions Involving
Scientific Notation
Simplify the expression. Write the answer in
scientific notation.
(2.6  104)(8.5  107)
(2.6)(8.5)  (104)(107)
22.1 
1011
Multiply 2.6 and 8.5 and add
exponents: 4 + 7 = 11.
2.21 
1012
Because 22.1 > 10, move the decimal
point left 1 place and add 1 to the
exponent.
Holt Algebra 2
1-5
Properties of Exponents
Check It Out! Example 4a
Simplify the expression. Write the answer in
scientific notation.
0.25  10–3
2.5 
Holt Algebra 2
10–4
Divide 2.325 by 9.3 and subtract
exponents: 6 – 9 = –3.
Because 0.25 < 10, move the decimal
point right 1 place and subtract 1 from
the exponent.
1-5
Properties of Exponents
HW pg. 39
#’s 30-38, 42, 45-50
Holt Algebra 2
1-5
Properties of Exponents
HW pg. 38
#’s 6-20, 43, 44
Holt Algebra 2