4.4 Simplifying Algebraic Expressions Involving Exponents Worksheet Page 5
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2
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4
5
6
7Sometimes it is necessary to express an expression involving radicals using
exponents in order to simplify it.
5
Representing an expression involving radicals
EXAMPLE
as a single power
!
5
a
8
b
3
x
! x
Simplify
.
3
Albino’s Solution
! x
8
Since this is a fifth root divided by a
5
a
8
b
3
5 a
b
3
x
5
! x
square root, I couldn’t write it as a
3
3
x
single radical.
2
8
3
2
I changed the radical expressions to
3
5 (x
)
5
2
exponential form and used exponent
16
15
2
3
rules to simplify.
5 (x
)
10
10
1
3
5 (x
)
10
3
When I got a single power, I
5 x
10
! x
converted it to radical form.
10
3
5
In Summary
Key Idea
• Algebraic expressions involving powers containing integer and rational
exponents can be simplified with the use of the exponent rules in the same
way numerical expressions can be simplified.
Need to Know
• When evaluating an algebraic expression by substitution, simplify prior to
substituting. The answer will be the same if substitution is done prior to
simplifying, but the number of calculations will be reduced.
• Algebraic expressions involving radicals can often be simplified by changing
the expression into exponential form and applying the rules for exponents.
CHECK Your Understanding
Simplify. Express each answer with positive exponents.
1.
5
m
4
3
3
2
x
(x
)
( y
)
a)
c)
e)
23
m
24
a
5
6
23
22
( p
) ( p)
f ) (k
)
b)
d)
22
a
Chapter 4 Exponential Functions
235
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