SAT Mc Graw Hill 2011

312 MCGRAW-HILL’S SAT

Concept Review 3

1. coefficient, base, and exponent
   2.multiplythe coefficients, keepthe bases, and add
   the exponents.
   3.dividethe coefficients, dividethe bases, and keep
   the exponents.
   4.multiplythe coefficients, multiplythe bases, and
   keepthe exponents.
   5.dividethe coefficients, keepthe bases, and sub-
   tractthe exponents.
   6.raisethe coefficient (to the power), keepthe base,
   and multiplythe exponents.
   7.− 4 x coefficient: −1; base: 4; exponent: x


2. (xy)−^4 coefficient: 1; base: xy;exponent: − 4

9.xy−^4 coefficient: x;base: y;exponent: − 4

10. (3x)^9 coefficient: 1; base: 3x;exponent: 9
    11.x^2 y− 9 x^2 y=− 8 x^2 y


11. 4x^3 + 2 x^5 + 2 x^3 =(4x^3 + 2 x^3 ) + 2 x^5 = 6 x^3 + 2 x^5


12. [(2)^85 +(3)^85 ] +[(2)^85 −(3)^85 ] =2(2)^85 =(2)^86


13. (3)^2 y(5)^2 y=(15)^2 y


14. 6(29)^32 ÷2(29)^12 =(6/2)(29)^32 −^12 =3(29)^20


15. 18(6x)m÷9(2x)m=(18/9)(6x/2x)m=2(3)m


16. (2x)m+^1 (2x^2 )m=(2m+^1 )(xm+^1 )(2m)(x^2 m) =
    (2^2 m+^1 )(x^3 m+^1 )


17. (3x^3 (8)^2 )^3 =(3)^3 (x^3 )^3 ((8)^2 )^3 = 27 x^9 (8)^6


18. (x^3 +y^5 )^2 =(x^3 +y^5 )(x^3 +y^5 ) =(x^3 )^2 + 2 x^3 y^5 +(y^5 )^2 =
    x^6 + 2 x^3 y^5 +y^10

Answer Key 3: Working with Exponentials

SAT Practice 3

1.B You don’t need to plug in g=−4.1. Just
simplify:

If

2.D(200)(4,000) =800,000 = 8 × 105

3.B 2 a^2 + 3 a− 5 a^2 = 9
Regroup: 3 a+(2a^2 − 5 a^2 ) = 9
Simplify: 3 a− 3 a^2 = 9
Factor: 3(a−a^2 ) = 9
Divide by 3: a−a^2 = 3

4.D 2 x= 10
Square both sides: (2x)^2 = 102
Simplify: 22 x= 100

5.B 5 x=y
Square both sides: (5x)^2 =y^2
Simplify: 52 x=y^2
Multiply by 5: 5(5^2 x) = 5 y^2
“Missing” exponents =1: 51 (5^2 x) = 5 y^2
Simplify: 52 x+^1 = 5 y^2

6.5/3 or 1.66 or 1.67
9 x= 25
Take square root:
Simplify: 3 x= 5
Divide by 3: 3 x÷ 31 =5/3
Simplify: 3 x−^1 =5/3 =1.66

9925 x

x

==

g

g

g

g

g

≠

−

()−

=

−

0 =−

3

3

3

9

1

3

2

2

2

, 2

7.B Begin by assuming n=m=1.

Then.

If nis multiplied by 4 and mis doubled, then

n = 4 and m= 2, so

which is half of the original value.

8.C (Remember that 2n× 2 nequals 2^2 n, or 4n, but

not 42 n!)

Cancel common factor 2n:

Simplify: 2 n−^1

9.A 3 m+ 3 m+ 3 m=3(3m) = 31 (3m) = 3 m+^1

2

2

n

22

22

nn

n

×

×

p

n

m

==

()

()

==

3 34

2

12

8

3

(^332)

,

p

n

m

==

()

()

=

3 31

1

333