Free Printable Algebra Test 4-1 Review - laws of exponents, radicals, sequences

1.

$\left(8x^3\right)\left(-7x^4y^3\right)$

a)

$\frac{8x^3}{7x^4y^3}$

b)

$x^7y^3$

c)

$-56x^7y^3$

d)

$\frac{8}{7xy^3}$

2.

$y^5\cdot y^9\cdot y^2$

a)

$16y$

b)

$y^{16}$

c)

$12y$

d)

$y^{12}$

3.

$\frac{8^9}{8^3}$

a)

$8^6$

b)

$\frac{1}{8^6}$

c)

$8^{12}$

d)

$\frac{1}{8^{12}}$

4.

$\frac{15x^9}{3x^6}$

a)

$12x^3$

b)

$5x^3$

c)

$\frac{x^3}{5}$

d)

$\frac{1}{12x^3}$

5.

$\frac{x^{10}y^{10}z^{10}}{x^3y^2z}$

a)

$x^{13}y^{12}z^{11}$

b)

$\frac{1}{x^7y^8z^9}$

c)

$x^7y^8z^9$

d)

$\frac{1}{x^{13}y^{12}z^{11}}$

6.

$\left(10m^4\right)^8$

a)

$10m^{12}$

b)

$10^8m^{12}$

c)

$10^8m^{32}$

d)

$10m^{32}$

7.

$\left(y^7\right)^4$

a)

$y^{11}$

b)

$y^{28}$

c)

$11y$

d)

$28y$

8.

$\left(4x^2y^3z\right)^3$

a)

$4x^5y^3z^3$

b)

$4^3x^5y^6z^3$

c)

$4x^6y^9z^3$

d)

$4^3x^6y^9z^3$

9.

$\left(wxyz\right)^6$

a)

$w^6x^6y^6z^6$

b)

$wxyz^6$

c)

$wx^3yz^3$

d)

$w^2x^2y^2z$

10.

$4^{-5}$

a)

$\frac{1}{20}$

b)

$-\frac{1}{20}$

c)

$\frac{1}{4^5}$

d)

$-\frac{1}{4^5}$

11.

$\frac{1}{y^{-6}}$

a)

$y^6$

b)

$-y^6$

c)

$-6y$

d)

$\frac{1}{-6y}$

12.

$6z^{-3}$

a)

$\frac{1}{6z^3}$

b)

$\frac{1}{-6z^3}$

c)

$\frac{6}{z^3}$

d)

$-\frac{6}{z^3}$

13.

$\frac{x^{-9}}{x^{10}}$

a)

$\frac{x^{10}}{x^9}$

b)

$\frac{x^9}{x^{10}}$

c)

$\frac{1}{x}$

d)

$\frac{1}{x^{19}}$

14.

$x^0$

a)

1

b)

0

c)

x

d)

100

15.

$\left(5y\right)^0$

a)

5

b)

5y

c)

1

d)

0

16.

$9t^0$

a)

1

b)

t

c)

9

d)

0

17.

Simplify (8y³)⁶

a)

8y¹⁸

b)

8⁶y¹⁸

c)

48y¹⁸

d)

8y⁹

18.

a)

2a²b⁶

b)

1/2a²b⁶

c)

b⁶/2a²

d)

2b⁶/a²

19.

a)

b)

c)

d)

20.

a)

b)

c)

d)

21.

a)

b)

c)

2x⁴y⁴

d)

2

22.

(2x²yz⁶) (6xy⁴z⁷)

a)

12x³y⁵z¹³

b)

12x³y⁴z¹³

c)

8x³y⁵z¹³

d)

8x³y⁴z¹³

23.

a)

x⁴y²z⁷

b)

y²z⁷

c)

x⁴y¹⁰z⁷

d)

24.

a)

b)

c)

d)

25.

a)

b)

c)

-64x⁷y¹²z²⁴

d)

26.

a)

b)

c)

d)

27.

a)

b)

c)

d)

28.

3x(x^-2y⁵z^-7)²

a)

b)

c)

d)

29.

Simplify:

a)

81√3

b)

9√3

c)

3√3

d)

√3

30.

Simplify: √(28xy²)

a)

2y√(7x)

b)

√(28xy²)

c)

y√(28x)

d)

7x√(2y)

31.

√(45x⁴y⁷)

a)

3x²y³√5

b)

9x²y³√(5y)

c)

3x²y³√(5y)

d)

3x⁴y⁷

32.

Simplify: √121p⁵r⁷s⁴?

a)

11prs √pr

b)

11p⁴r⁶s²√pr

c)

11p²r³s²√pr

d)

11p²r³s²

33.

Simplify:
6√2 ⋅5√14

a)

32√7

b)

60√7

c)

2√7

d)

30√7

34.

2√5 + 4√5 =

a)

6√10

b)

8√10

c)

8√5

d)

6√5

35.

Simplify:

a)

8x⁹

b)

8x³

c)

8x⁴√x

d)

8x³√x

36.

Simplify the expression:

a)

8√6

b)

6√6

c)

8√5

d)

64√6

37.

Simplify the radical expression:
$\sqrt{2x^2y^3}$

a)

$2y\sqrt{xy}$

b)

$2x\sqrt{y^2}$

c)

$y\sqrt{2xy}$

d)

$xy\sqrt{2y}$

38.

Simplify the radical expression:
$\sqrt{128a^3b^4}$

a)

$8ab^2\sqrt{2a}$

b)

$2a\sqrt{8ab^2}$

c)

$2ab\sqrt{64ab}$

d)

$64ab^2\sqrt{2a}$

39.

Simplify the radical:
$\sqrt{98}$

a)

$2\sqrt{7}$

b)

$7\sqrt{2}$

c)

$14\sqrt{2}$

d)

$49\sqrt{2}$

40.

Simplify the radical expression:
$\sqrt{27m^7p^{4\ }}$

a)

$3m\sqrt{3m^3p^2}$

b)

$3m^3p^2\sqrt{3m}$

c)

$9mp\sqrt{3m}$

d)

$9m^3p^2\sqrt{3m}$

41.

Simplify the radical expression:
$\sqrt{x^3y^5z^2}$

a)

$xy^2z$

b)

$x^2y^4z^2\sqrt{xy}$

c)

$xy^2z\sqrt{xy}$

d)

$xyz\sqrt{xy}$

42.

Simplify the radical expression:
$\sqrt{151r^2s^3}$

a)

$rs\sqrt{151s}$

b)

$151rs\sqrt{s}$

c)

$10rs\sqrt{15s}$

d)

$r^2s^2\sqrt{151s}$

43.

Simplify the radical expression:
$2\sqrt{48}$

a)

$4\sqrt{3}$

b)

$8\sqrt{3}$

c)

$2\sqrt{3}$

d)

$3\sqrt{8}$

44.

Simplify the radical expression:
$\sqrt{92a^2b^3}$

a)

$23ab\sqrt{2b}$

b)

$2ab\sqrt{23b}$

c)

$4ab\sqrt{23b}$

d)

$4a^2b^2\sqrt{23b}$

45.

Simplify the radical expression:
$\sqrt{289c^5}$

a)

$17c^2\sqrt{c}$

b)

$17c^4\sqrt{17c}$

c)

$28c^2\sqrt{9c}$

d)

$34c^2\sqrt{c}$

46.

Simplify the radical:
$7\sqrt{124}$

a)

$2\sqrt{31}$

b)

$7\sqrt{31}$

c)

$14\sqrt{31}$

d)

$28\sqrt{31}$

47.

Simplify the radical expression:
$2\sqrt{56a^2b^2}$

a)

$4ab\sqrt{14}$

b)

$2ab\sqrt{14}$

c)

$14ab\sqrt{2ab}$

d)

$14\sqrt{2ab}$

48.

Find the common ratio for the geometric sequence.

a)

10

b)

1/2

c)

2

d)

4

49.

Is the sequence -432, 72, -12, 2,...geometric?

a)

yes

b)

no

50.

What are the next 3 terms in the following geometric sequence:

512, 256, 128, ___, ___, ___, ...

a)

1024, 2048, 4096

b)

32, 8, 2

c)

64, 32, 16

d)

92, 66, 38

51.

Write the explicit formula for the geometric sequence.

a)

a_n = 4(3)^n-1

b)

a_n = 3(4)^n-1

c)

a_n = -4(3)^n-1

d)

a_n = 3(-4)^n-1

52.

This image shows how a certain bacteria grows in a petri dish. What is the common ratio of this sequence?

a)

4

b)

3

c)

2

d)

6

53.

Find the first four terms of the sequence given the rule:
a_n = 4(5)^n-1

a)

20, 100, 500, 2500

b)

5, 20, 80, 320

c)

4, 20, 100, 500

d)

4, 9, 14, 19

54.

What is the 14th term of the geometric sequence?

a)

14,348,907

b)

4,782,969

c)

1,594,323

d)

45

55.

Given the sequence:

125, 25, 5, ....

Write the rule a_n using the geometric sequence formula:

a)

a_n = (125)(1/5)^(n-1)

b)

a_n = 625(1/5)^(n-1)

c)

a_n = 625(5)^(n-1)

d)

a_n = 125 + 5n

56.

Find a₁₂ in the sequence -1, -3, -9, -27, ...

a)

-177,147

b)

-19,683

c)

-59,049

d)

118,098

57.

The rule for finding a_n of a geometric sequence is

a_n = 10(2)^n-1_{What is the common ratio(r) of the sequence?}

a)

²

b)

¹⁰

c)

²⁰

d)

2ⁿ

58.

A geometric sequence has a common ration(r) of 3 and the 8th term (a₈) is 13,122. What is the first term of the sequence (a₁)?

a)

3

b)

6

c)

18

d)

2

59.

What is the 9^th term in a geometric sequence with a common ratio of 2 and a first term of 3?

a)

384

b)

768

c)

1,536

d)

27

60.

Daisy received $2 on her first birthday. Each year, the amount of money she received tripled. How much money will she receive on her 5^th birthday?

a)

$10

b)

$300

c)

$162

d)

$416

Algebra Test 4-1 Review - laws of exponents, radicals, sequences

Total questions: 60

Worksheet time: 4hrs 34mins

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