Sat math Essentials

e.
72
Answer
b.
Answer choice 
a
is incorrect because 2
3
3
2
9
. Answer choice 
c
is incorrect because 
2
3
. Answer choice 
d
is incorrect because you cannot combine radicals with different radi-
cands using addition or subtraction. Answer choice 
e
is incorrect because 
72
2
36
6
2
.
Answer choice 
b
is correct because 
24
6
4
2
6
.
2
9
3
2
9
3
24
8
a
b
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N U M B E R S A N D O P E R AT I O N S R E V I E W
–
4 5

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N e g a t i v e E x p o n e n t s
Negative exponents are the opposite of positive exponents. Therefore, because positive exponents tell you how many
of the base to 
multiply
together, negative exponents tell you how many of the base to 
divide
.
a
n
a
1
n
3
2
3
1
2
3
1
3
1
9
5
3
5
1
3
5
1
5
5
1
1
25
Practice Question
Which of the following is equivalent to 
6
4
?
a.
1,296
b.
1,2
6
96
c.
1,2
1
96
d.
1,2
1
96
e.
1,296
Answer
c.
6
4
6
1
4
6
6
1
6
6
1,2
1
96
R a t i o n a l E x p o n e n t s
Rational numbers are numbers that can be written as fractions (and decimals and repeating decimals). Similarly,
numbers raised to rational exponents are numbers raised to fractional powers:
4
1
2
25
1
2
8
1
3
3
2
3
For a number with a fractional exponent, the numerator of the exponent tells you the power to raise the num-
ber to, and the denominator of the exponent tells you the root you take.
4
1
2
4
1
4
2
The numerator is 1, so raise 4 to a power of 1. The denominator is 2, so take the square root.
25
1
2
25
1
25
5
The numerator is 1, so raise 25 to a power of 1. The denominator is 2, so take the square root.
8
1
3
3
8
1
3
8
2