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DSPM 0800 CHAPTER 11 REVIEW
Simplify. Write answers with positive exponents:
3
x x
Use the product rule:
3 3 1
2
2
(By definition, a negative power is the reciprocal
of a positive power. To change negative powers
to positive, mo
x x x
x
x
ve the negative power to the other
side of the fraction bar)
12 0 19
y y y
12 0 19 12 0 19 0
31
y y y y (The y is actually 1; a factor that is equal to 1 can be dropped)
y
8
2
x
x
Use the quotient rule:
8
8 2
2
6
x
x
x
x
7
7
m
m
7
7 7
7
0
m
m
m
m
9 3
( x )
Use the power-of-a-power rule:
9 3 9(3)
27
( x ) x
x
2 3
(3 xy )
Use the power-of-a-product rule:
2 3 3 3 2 3
3 6 3 2 3
27 (Evaluate 3 27. Use power-of-a-power rule for ( ) )
xy x y
x y y
3 2
a
b
Use the power-of-a-quotient rule:
3 2 2 3
3
6
3
a ( a )
b b
a
b
5 3 2
( 3 x y )
Note that with powers of a negative base, the exponent determines whether the
result is positive or negative. An even power will be positive, an odd power
will be negative.
5 3 2 2 5 2 3 2
10 6
10
6
x y x y
x y
x
y
2 4 3 2 7
( 5 )( 7 )
xy z x y z
2 4 3 2 7 1 ( 3) 2 ( 2) 4 7
2 0 11
11
2
xy z x y z x y z
x y z
z
x
3 4
7 8
x y
x y
Divide the coefficients using the signed number rules and divide the variables
using the laws of exponents.
3 4
7 8
x y
x y
1
3 7 4 8
1
4 4
4 4
x y
x y
x y
4 2
5 x (3 x 7 x 10)
Use the distributive property. If the first factor is negative, remember to watch
the pattern of signs.
4 2 4 2 4 4
6 5 4
x x x x x x x x
x x x
- (5^ x^ ^ 6)(3^ x 7)
Use the FOIL method.
2
2
x x x x x x
x x x
x x
2
(2 x 9)
The binomial square results in the perfect square trinomial.
2 2 2
2
x x x
x x
2
( x 2)( x 3 x 8)
Multiplying general trinomials is an extension of the FOIL method.
2 2 2
3 2 2
3 2
x x x x x x x x x x
x x x x x
x x x
5 4 3
3
x x x
x
Divide each term of the numerator by the denominator.
5 4 3 5 4 3
3 3 3 3
2
x x x x x x
x x x x
x x
