4.4 Simplifying Algebraic Expressions Involving Exponents Worksheet Page 3
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1
2
3
4
5
6
7APPLY the Math
2
Connecting the exponent rules to the
EXAMPLE
simplification of algebraic expressions
2
3
23
(2x
y
)
Simplify
.
2
3
(x
y
24
)
Adnan’s Solution
I used the product-of-powers rule to
23
2
3
3
23
3
2
3
(2 x
y
)
(2)
(x
)
( y
)
5
raise each factor in the numerator
3
2
3
2
2
24
24
(x
y
)
(x
)
( y
)
to the third power and to square
each factor in the denominator.
Then I multiplied exponents.
6
29
8x
y
5
I simplified the whole expression by
6
28
x
y
subtracting exponents of terms with
62 (28)
2926
5 8x
y
the same base.
14
215
5 8x
y
One of the powers had a negative
exponent. To write it with positive
14
8y
5
exponents, I used its reciprocal.
15
x
3
Selecting a computational strategy
EXAMPLE
to evaluate an expression
2n11
3n21
(x
) (x
)
Evaluate the expression
for
x 5 23
and
n 5 2.
2n25
x
Bonnie’s Solution: Substituting, then Simplifying
I substituted the values for x
2n11
3n21
2(2) 11
3(2) 21
(x
) (x
)
(23)
(23)
5
and n into the expression.
2n25
2(2) 25
x
(23)
Then I evaluated the
5
5
(23)
(23)
numerator and denominator
5
21
(23)
separately, before dividing
one by the other.
(2243) (2243)
5
1
23
5 2177 147
Chapter 4 Exponential Functions
233
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