Free Printable ALG Unit 6 Day 4 Practice

1.

In Product of Powers property what do you do to the exponents?

a)

add

b)

subtract

c)

multiply

d)

divide

2.

In Power of Powers property what do you do to the exponents?

a)

add

b)

subtract

c)

multiply

d)

divide

3.

Which property rule does this expression follow?

$5^2\ \cdot\ 5^8$

a)

Product of Powers

b)

Power of Powers

4.

Which property rule does this expression follow?

$\left(7^5\right)^2$

a)

Product of Powers

b)

Power or Powers

5.

Simplify the expression

8^7\cdot8^2

a)

$8^{14}$

b)

$8^9$

6.

Simplify the expression

$\left(12^2\right)^4$

a)

$12^6$

b)

$12^8$

7.

Simplify the expression

$12^4\cdot12^{15}$

a)

$12^{19}$

b)

$12^{60}$

8.

Simplify the expression

$\left(52^5\right)^4$

a)

$52^9$

b)

$52^{20}$

9.

The Power of Products Property says when the exponents are the same and the bases are different, you ________________________

a)

add the bases

b)

multiply the bases

c)

multiply the exponents

d)

add the exponents

10.

What is the EXPONENT in the power written below?

4

a)

0

b)

4

c)

1

d)

2

11.

Simplify:

$t^9\cdot t^8$

a)

$t^1$

b)

$t^{72}$

c)

$t^{17}$

d)

None of the above

12.

Simplify the expression: $3^3\times4^3$

a)

$12^9$

b)

$12^3$

c)

$12^6$

d)

$7^6$

13.

Find the missing exponent:

$3^{16}=3^8\cdot3^?$

a)

2

b)

8

c)

4

d)

1

14.

The Product of Powers Property says when the base is the same and the exponent is different you should ________________________

a)

add the bases

b)

multiply the bases

c)

add the exponents

d)

multiply the exponents

15.

Simplify:

$7^8\cdot7$

a)

$7^9$

b)

$49^8$

c)

$7^8$

d)

None of the above

16.

True or False $7\times7^{8\ }$ is equivalent to $7^4\times7^5$

a)

True

b)

False

17.

According to exponent rules, when we multiply the same base we _______ the exponents.

a)

Multiply

b)

Add

c)

Divide

d)

Subtract

18.

Solve using the product law of exponents

(5⁵)(5³)

a)

25⁸

b)

5¹⁵

c)

25¹⁵

d)

5⁸

19.

Simplify the expression.
x⁴ (x¹²)

a)

x³

b)

x⁴⁸

c)

x¹⁶

d)

x⁸

20.

Simplify (c⁵)(c³)(c³)

a)

c⁴⁵

b)

3c¹¹

c)

c¹¹

d)

3c⁴⁵

21.

Simplify:
(x³y²)(xy⁴)

a)

x³y⁸

b)

x⁴y⁶

c)

x³y⁶

d)

x⁴y⁸

22.

^simplify (5x³)(2x²)

a)

10x⁵

b)

3x

c)

10x⁶

d)

7x⁵

23.

Simplify (-4r⁵)(2r⁸)

a)

-8r¹³

b)

-2r¹³

c)

-8r⁴⁰

d)

-2y⁴⁰

24.

Quotient Rule states: keep the base the same and do this to the exponents.

a)

multiply

b)

add

c)

subtract

d)

divide

25.

a)

y¹⁵

b)

y⁵⁰

c)

y²

d)

y⁵

26.

a)

x²

b)

x³

c)

x

d)

x⁵

27.

a)

2a⁴b⁴

b)

4a³b⁴

c)

4a⁸b⁵

d)

2a⁴b³

28.

$\frac{18w^{15}v^{10}}{6w^3v^2}$

a)

$12w^{12}v^8$

b)

$3w^{12}v^8$

c)

$3w^5v^5$

d)

$12w^5v^5$

29.

According to exponent rules, when we raise a power to a power we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

30.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

31.

True or False:

a)

True

b)

False

32.

Simplify the expression.

a)

7⁶

b)

7^-5

c)

1/7⁵

d)

7⁵

33.

Simplify the expression.

a)

1²²

b)

1³⁰

c)

6²²

d)

6³⁰

34.

Quotient Rule states: keep the base the same and do this to the exponents.

a)

multiply

b)

add

c)

subtract

d)

divide

35.

True or False?

a)

True

b)

False

36.

According to exponent rules, when we multiply powers we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

37.

According to exponent rules, when we divide powers we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

38.

Which is the expanded form of
5³

a)

3 x 3 x 3

b)

5 x 5

c)

5 x 5 x 5

d)

5 x 3

39.

What is the exponential form of
4 x 4 x 4 x 4 x 4 x 4

a)

6⁴

b)

4²

c)

4⁶

d)

4 x 6

40.

Simplify the expression:
(5⁸) ÷ (5²)

a)

5⁶

b)

5¹⁰

c)

5⁴

d)

5¹⁶

41.

(3⁴)(3⁷)

a)

3²⁸

b)

3³

c)

3^-3

d)

3¹¹

42.

Which number is the BASE?
2³= 8

a)

2

b)

3

c)

8

43.

Billy was asked to solve 3⁵∙3⁴. He got 9²⁰. What error did he make?

a)

When he multiplies exponents, he is supposed to add the base and the exponent

b)

When he multiplies exponents, he is supposed to multiply the base and keep the exponents

c)

When he multiplies exponents, he is supposed to keep the base and add the exponents if the base is the same

d)

None of the above

44.

Simplify the following expression:

3x⁴ ⋅ 6x⁶

a)

18x¹⁰

b)

9x¹⁰

c)

18x²⁴

d)

9x²⁴

45.

Simplify the expression.

a)

b⁵

b)

b

c)

b^-1

d)

b⁶

46.

Simplify the expression.
(6x²)(-3x⁵)

a)

18x⁷

b)

-18x⁷

c)

18x⁷

d)

3x⁷

47.

Simplify: $\frac{a^{14}b^4c^5}{a^4b^2c^3}$

a)

$a^{18}b^6c^8$

b)

$a^{14}b^4c^5$

c)

$a^{10}b^2c^2$

d)

$a^{13}b^3c^4$

48.

Simplify: $x^8y^2z^2\cdot xyz$

a)

$x^8y^2z^2$

b)

$x^{9^{ }}y^3z^3$

c)

$xyz^{12}$

d)

$xyz^{15}$

49.

Simplify: $\frac{x^8y^4}{x^2}$

a)

$x^{10}y^4$

b)

$x^{16}y^4$

c)

$x^6y^4$

d)

$x^6y^2$

50.

Simplify: $\frac{a^{17}b^{10}}{a^2b^7}$

a)

$a^{34}b^{70}$

b)

$a^{15}b^{17}$

c)

$a^{19}b^3$

d)

$a^{15}b^3$

51.

Simplify: $\frac{x^2y^8}{xy}$

a)

$xy^7$

b)

$xy$

c)

$x^3y^9$

d)

$x^3y^7$

52.

Simplify: $\frac{m^{10}}{m^2}$

a)

$m^{20}$

b)

$m^{12}$

c)

$m^8$

d)

$m^5$

53.

Simplify: $2x^5\cdot5x^6$

a)

$25x^{11}$

b)

$10x^{11}$

c)

$7x^{11}$

d)

$10x^{30}$

54.

Simplify: $h^3\cdot g^2\cdot h^5$

a)

$g^2\cdot h^8$

b)

$gh^{10}$

c)

$g^2\cdot h^{15}$

d)

$h^8$

55.

Simplify (-4r⁵)(2r⁸)

a)

-8r¹³

b)

-2r¹³

c)

-8r⁴⁰

d)

-2y⁴⁰

56.

a)

32t¹¹r⁸

b)

32t³⁰r¹⁵

c)

-32t³⁰r¹⁵

d)

-32t¹¹r⁸

57.

Simplify the exponential expression:

a)

10x^-2

b)

2x²

c)

2x¹²

d)

10x¹²

58.

Simplify
(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

59.

Simplify the expression.
(x⁵ )(x⁵)

a)

x¹⁰

b)

x²⁵

c)

x¹⁶

d)

x⁸

60.

(6x²)(-3x⁵)

a)

18x⁷

b)

-18x⁷

c)

18x⁷

d)

3x⁷

61.

(2m⁴)(5m²)

a)

10m⁶

b)

10m⁸

c)

7m⁶

d)

7m⁸

62.

Simplify the following:
(x²y)⁵

a)

x⁷y⁵

b)

x²y⁵

c)

x¹⁰y⁵

d)

x⁵y⁵

63.

(5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

64.

Simplify the exponential expression.

a)

2x⁶y¹²

b)

2x⁵y⁷

c)

8x⁶y¹²

d)

8x⁵y⁷

65.

(2ab)³

a)

2³a³b³

b)

2ab³

c)

6a³b³

d)

6ab

66.

a)

a⁷

b)

a¹⁰

c)

a³

d)

a^-3

67.

Expand x⁵

a)

x⋅x⋅x⋅x⋅x

b)

1/x⋅x⋅x⋅x⋅x

c)

x⁵

d)

5

68.

Simplify: (5p⁹q³)(2pq⁷)

a)

7p¹⁰q¹⁰

b)

10p⁹q²¹

c)

10p¹⁰q¹⁰

d)

10p⁸q^-4

69.

a)

x³

b)

x⁹

c)

x

d)

1

70.

Simplify: x ∙ x ∙ x ∙ x ∙ x ∙ x

a)

x⁶

b)

6x

c)

x³

d)

6x⁶

71.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

72.

^simplify 5x³2x²

a)

10x⁵

b)

3x

c)

10x⁶

d)

7x⁵

73.

9x⁵y²⋅ 9xy²

a)

81x⁶y⁴

b)

81x⁵y⁶

c)

9x⁶y⁴

d)

none of the above

74.

8x⁵y³⋅ 10xy³

a)

80xy³

b)

80x⁵y⁹

c)

80x⁶y⁶

d)

none of the above

75.

Quotient Rule of Exponents: When dividing exponents, if the bases are the same, then you....

a)

Multiply the exponents

b)

Subtract the exponents

c)

Add the exponents

d)

Divide the exponents

76.

$\frac{a^6b^4}{a^2b^3}$

a)

ab

b)

a⁸b⁷

c)

a³b¹

d)

a⁴b

77.

$\frac{14x^2y^2}{2xy}$

a)

7xy

b)

7x²y²

c)

2x³y³

d)

2

78.

$\frac{-36a^2b^5}{4a^2b^3}$

a)

-9b²

b)

9b²

c)

-9a

d)

9ab

79.

$\frac{8a^6b^{12}}{4a^3b^7}$

a)

2a³b⁵

b)

a³b⁵

c)

2a⁹b¹⁹

d)

2ab⁵

80.

$\frac{9a^3b^5}{-3ab^2}$

a)

$-3a^3b^3$

b)

$-3a^4b^7$

c)

$12a^2b^3$

d)

$-3a^2b^3$

81.

$\frac{a^4}{a^{12}}$

a)

$a^3$

b)

$a^{16}$

c)

$\frac{1}{a^3}$

d)

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

82.

$\frac{x^{18}y^{15}}{x^6y^3}$

a)

$x^3y^5$

b)

$x^{12}y^{12}$

c)

$x^{24}y^{18}$

d)

$x^{108}y^{45}$

83.

$\frac{45x^6y^9}{5x^4y^7}$

a)

$9x^2y^2$

b)

$40x^2y^7$

c)

$\frac{9x^2}{y^7}$

d)

$\frac{9x^{10}}{y^{11}}$

84.

$\frac{24a^4b^8}{12a^2b^2}$

a)

$2a^2b^6$

b)

$\frac{1}{2a^2b^6}$

c)

$\frac{b^6}{2a^2}$

d)

$\frac{2b^6}{a^2}$

85.

Simplify: $\frac{x^9}{x^2}$

a)

$x^{11}$

b)

$x^7$

c)

$x^{18}$

d)

$x^{92}$

86.

Simplify:

a)

4p³

b)

3p³

c)

1/3p⁴

d)

3p⁴

87.

Simplify:

a)

$3k^9$

b)

$\frac{k}{3}$

c)

$\frac{k}{6}$

d)

$6k$

88.

According to exponent rules, when we multiply the same base we _______ the exponents.

a)

Multiply

b)

Add

c)

Divide

d)

Subtract

89.

According to exponent rules, when we divide the expressions we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

90.

According to exponent rules, when we raise the coefficients to a power we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

91.

Simplify:

a)

4x⁸

b)

4x²

c)

4x¹⁴

d)

2.5x²

92.

a)

8x⁴

b)

8x⁸

c)

6x⁴

d)

6x⁸

93.

Application:
What is the area of the rectangle with the given sides?

a)

7x³y⁸z⁴

b)

10x²y¹⁶z³

c)

10x³y⁸z⁴

d)

none of the above

94.

What's the base?
y⁵

a)

5

b)

y

95.

Simplify (-1/2)⁰

a)

1

b)

0

c)

-1

d)

-2

96.

Simplify: (2x³y⁵)³

a)

8x⁹y¹⁵

b)

6x⁹y¹⁵

c)

2x⁹y¹⁵

d)

8x⁶y⁸

97.

Simplify using exponent rules.

a)

32x³y⁴

b)

32x⁹y¹³

c)

16x⁸y¹²

d)

16x⁶y⁷

98.

Which statement is correct?

a)

1⁰ = 1

b)

0¹= 1

c)

1⁰ = 0

d)

0⁰ = 1

99.

Simplify.

a)

y¹⁵

b)

y⁵

c)

y²

d)

2y⁵

100.

Simplify (-9)⁰

a)

-9

b)

-1

c)

1

d)

9

101.

How would you simply (2x⁵)(6x⁴) ?

a)

MULTIPLY both the coefficients and MULTIPLY the exponents

b)

DIVIDE the coefficients then SUBTRACT the exponents

c)

Combine like terms

d)

MULTIPLY the coefficients then ADD exponents

102.

(2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

103.

Simplify using exponent rules.

a)

19,683y³

b)

243y³

c)

y³/243

d)

y³/19,683

ALG Unit 6 Day 4 Practice

Total questions: 103

Worksheet time: 26hrs 45mins

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