Rules for Exponents 81
(xy+ )^2 ≠xxy^22 +y! (xy+ )^2 =(xyx+ )(xy+ )^
=xxx^22 + xyyyy+ (which you will learn in
Chapter 9). This is the most common error
that beginning algebra students make.b. ()xy+^2
Step 1. This is a power of a sum. It cannot
be simplifi ed using only rules for
exponents.()xy+(^2) is the answer.
c. ()xy^2
Step 1. This is a power of a difference. It cannot be simplifi ed
using only rules for exponents.
()xy
(^2) is the answer.
d. ()xy+^23 ()()xy+
Step 1. This is a product of expressions with
the same base, namely, ()xy+. Keep
the base and add the exponents.
()xy+ ()xy+ =()xyx+ =()xyx+
23
()
23 + 5
Step 2. ()y^5 is a power of a sum. It can-
not be simplifi ed using only rules for exponents.
()xy+
5
is the answer.
e. ()
xy
()xy
5
2
Step 1. This is a quotient of expressions with the same base, namely, ()y.
Keep the base and subtract the exponents.
()xy
()xy
=()xyx =()xyx
5
2
52 − 3
Step 2. ()y^3 is a power of a difference. It cannot be simplifi ed using only
rules for exponents.
()xy
3
is the answer.
( )^2 ≠xyx^22 y!
When a quantity enclosed in a grouping
symbol acts as a base, you can use the
rules for exponents to simplify as long
as you continue to treat the quantity as
a base.