Exponents and Roots

SSAT Exponents and Roots Drill 1

  1.

(A)   (x²)

(B)   x²⁴

(C)   x⁵

(D)   x²

(E)   24x

  2. Simplify the variable expression:

(A)   

(B)   

(C)   

(D)   

(E)   

  3.

(A)     

(B)     

(C)   

(D)   

(E)   

  4. Calculate 3a – b² when a = 6 and b = 4.

(A)   0

(B)   1

(C)   2

(D)   14

(E)   34

  5. If (x^a)³ = x¹⁵ and = x⁷, then b − a =

(A)   –4

(B)   –2

(C)   2

(D)   4

(E)   14

  6. If abc ≠ 0, a⁰ + b⁰ + c⁰ =

(A)   abc

(B)   0

(C)   1

(D)   3

(E)   It cannot be determined from the information given.

  7. If 0 < x < 1, which of the following inequalities is correct?

(A)    < x < x²

(B)   x² < x <

(C)   x < x² <

(D)    < x² < x

(E)   x < < x²

  8. (2.4 × 10^x)(3.0 × 10^y) =

(A)   72 × 10^{x + y}

(B)   7.2 × 10^{x + y}

(C)   7.2 × 10^{x + y + 1}

(D)   7.2 × 10^xy

(E)   72 × 10^xy

  9. 100,000 + (4.0 × 10³) =

(A)   4,000

(B)   10,040

(C)   10,400

(D)   100,400

(E)   104,000

10. =

(A)   3

(B)   9

(C)   9

(D)   18

(E)   81

SSAT Exponents and Roots Drill 2

  1. Simplify the variable expression: (–2x²y⁵)³

(A)   –2x⁵y⁸

(B)   –2x⁶y¹⁵

(C)   –6x⁶y¹⁵

(D)   –8x⁶y¹⁵

(E)   8x⁶y¹⁵

  2. Calculate a²b – ab² + (ab)² when a = 5 and b = 2.

(A)   20

(B)   50

(C)   100

(D)   130

(E)   170

  3. Simplify the variable expression:

(A)   4x³y^–3

(B)   2x³y^–3

(C)   x³y^–3

(D)   y^–3

(E)   x⁻³y⁻⁷

  4. =

(A)   (x)

(B)   x¹⁵

(C)   x²

(D)   

(E)   (x²)

  5. =

(A)   

(B)   

(C)   

(D)   9

(E)   16

  6. =

(A)   64

(B)   32

(C)   16

(D)   8

(E)   4

  7. Simplify the variable expression:

(A)   

(B)   

(C)   

(D)   a

(E)   b

  8. Calculate (x)(x²) when x = –4.

(A)   64

(B)   16

(C)   4

(D)   –16

(E)   –64

  9.

(A)   25

(B)   10

(C)   5

(D)   

(E)   

10. Simplify the variable expression:

(A)   a²b⁸

(B)   a⁸b³

(C)   a⁸b²⁰

(D)   a²b⁵

(E)   

ISEE Exponents and Roots Drill 1

  1. What is the value of the expression ?

(A)   

(B)   

(C)   2

(D)   4

  2. What is the value of the numerical expression 5.3 × 10⁶ + 6.2 × 10⁴?

(A)   6.152 × 10⁴

(B)   5.92 × 10⁵

(C)   5.362 × 10⁶

(D)   1.25 × 10¹⁰

  3. Which expression is equivalent to the expression ?

(A)   18x³

(B)   18x⁶

(C)     6x³

(D)     6x⁶

  4. =

(A)   6²

(B)   6⁴

(C)   6¹⁶

(D)   6³²

  5. (–2x²y³)⁴ =

(A)   –16x⁸y¹²

(B)   –16x⁶y⁷

(C)   16x⁶y⁷

(D)   16x⁸y¹²

  6. If 81³ = 3^x, then x =

(A)     9

(B)   12

(C)   27

(D)   30

  7. = ?

(A)   0

(B)   1

(C)   

(D)   

  8. Which expression is equivalent to the expression shown?

(A)   12 + 18x

(B)   36x

(C)   

(D)   30x²

  9. The approximate distance around the equator of the Earth, which is 2.5 × 10⁴ miles, is about how many times the approximate distance from Detroit, MI to Cleveland, OH, which is 5.0 × 10¹ miles?

(A)   2.0 × 10⁶

(B)   5.0 × 10⁴

(C)   2.0 × 10⁴

(D)   5.0 × 10²

10. = ?

(A)   1.6 × 10¹²

(B)   1.6 × 10⁸

(C)   1.6 × 10⁷

(D)   1.6 × 10⁴

ISEE Exponents and Roots Drill 2

  1. If x and y are both integers, what is (8.0 × 10^x)(6.0 × 10^y) expressed in scientific notation?

(A)   48.0 × 10^xy

(B)     4.8 × 10^{x + y + 1}

(C)     4.8 × 10^{x + y}

(D)     4.8 × 10^xy

Directions: Using all information given in each question, compare the quantity in Column A to the quantity in Column B. All questions in Part Two have these answer choices:

(A)   The quantity in Column A is greater.

(B)   The quantity in Column B is greater.

(C)   The two quantities are equal.

(D)   The relationship cannot be determined from the information given.

 

 

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