SAT Mc Graw Hill 2011

436 McGRAW-HILL’S SAT

5. E

Simplify numerator (add exponents):

Simplify quotient

(subtract exponents):

Simplify exponent: x5/2

Rewrite as a root:

6. C x=a^5 =b^3
   Solve for a(raise to the 1/5): x1/5=a
   Solve for b(raise to the 1/3): x1/3=b
   Multiply aand b: ab=x1/5×x1/3
   Simplify (add exponents): ab=x1/5 +1/3
   Simplify: ab=x8/15
   (Remember the quick way to add fractions:
   “zip-zap-zup” from Chapter 7, Lesson 3.)

x

5

x^42 −−(/)^12

x

x

42

− 12

xx

x

3

2

1

2

1

2

×

=

−

Concept Review 6

1. 5−^2 =1/(5^2 ) =1/25


2. 
   


3. 2−^5 =1/(2^5 ) =1/32


4. 
   

5.

6. (16/25)−3/2=1/(16/25)3/2=(25/16)3/2=((25/16)1/2)^3

7.

8.

9. 4x−^2 =4/x^2


10. (4y)−^2 =1/(4y)^2 =1/(16y^2 )


11. 99 327

32 123 3

()mm mmm=⎝⎛()⎞⎠ =()=

442

12

()ggg==

xx^13 =^3

=

⎛

⎝

⎜

⎞

⎠

⎟ =

⎛

⎝⎜

⎞

⎠⎟

=

25

16

5

4

125

64

(^33)

4432 12 428

(^333)
=()=()==

25 −^12 =1 25()^12 ==1 25 1 5

99312 ==

12.

13. x3/4=^27
    Raise both sides to the
    4/3 power: (x3/4)4/3= 27 4/3
    Simplify: x^1 =(271/3)^4
    Simplify: x= 34
    Simplify: x= 81


14. b−1/2=^4
    Raise both sides to the
    −2 power: (b−1/2)−^2 = 4 −^2
    Simplify: b^1 =1/(4^2 )
    Simplify: b=1/16


15. (2m)−^6 =^16
    Simplify: 2 −^6 m= 16
    Raise to the −1/2 power: 23 m= 16 −1/2
    Simplify: 23 m=
    Simplify: 23 m=1/4

116

27 9 27 9 3 3

9

(^131213121312)
1
bb b b bb
b

( ) ( ) =( ) ×( ) =×

=

−

(^66) = 96 b
Answer Key 6:
Negative and Fractional Exponents
SAT Practice 6

1. 1/20 or 0.05 4 −n=1/4n=1/20


2. B 54 ×m=^52
   Divide by 5^4 : m= 52 /5^4
   Simplify (subtract exponents): m= 5 −^2


3. 1/4 or 0.25 2 m× 2 m× 2 m× 2 m= 2
   Simplify (add exponents): 24 m= 2
   Exponents must be equal: 4 m= 1
   Divide by 4: m=1/4

4. A

Write as powers of 3:

Simplify denominator:

Divide numerator and

denominator by 3^2 n:3^1 /1 =^3

Perhaps a simpler method is to simply pick nto be

0 (because ncan be any number). This gives

(3 × 30 )/9^0 =(3 ×1)/1 =3. The only choice that

equals 3 when n=0 is (A).

33

3

12

2

× n

n

33

3

12

2

×

()

n

n

33

9

×^2 n

n