Free Printable Module 1 Cumulative Review: Eureka Math 8

1.

(-2)(-2)(-2)

a)

(2)³

b)

(-2)⁴

c)

(-2)³

2.

(⅓)(⅓)

a)

⅓

b)

(⅓)²

c)

(⅓)¹

3.

Simplify: x ∙ x ∙ x ∙ x ∙ x ∙ x

a)

x⁶

b)

6x

c)

x³

d)

6x⁶

4.

What number is the base in the following: 8⁶

a)

6

b)

86

c)

68

d)

8

5.

a)

$7^4$

b)

$4^7$

c)

$x^4$

d)

$7^x$

6.

a)

12

b)

15

c)

x

d)

2

7.

(7 x 100,000) + (3 X 1000) + (7 X 100) + (5 X 10) + (3 X 1) = ________

a)

703, 701

b)

737,531

c)

703, 751

d)

703, 753

8.

What is the following expression in standard form?

7\times10^3+2\times10^1+3\times10^0+5\times10^{-1}

a)

7,235

b)

-7,023.5

c)

723.5

d)

7,023.5

9.

Find the expanded form with exponential notation of 3.5

a)

$3\times10^0+5\times10^{-1}$

b)

$3\times10^3+5\times10^{-5}$

c)

$3\times10^1+5\times10^0$

d)

$3+0.5$

10.

Find the expanded form with exponential notation of 167

a)

$1\cdot10^0+6\cdot10^{-1}\cdot7\cdot10^{-2}$

b)

$1\cdot10^2+6\cdot10^1+7\cdot10^0$

c)

$1\cdot10^2\cdot6\cdot10^1\cdot7\cdot10^0$

d)

$10^1+10^6+10^7$

11.

According to the laws of exponents, when multiplying keep the base and __________ the exponents.

a)

Multiply

b)

Add

c)

Divide

d)

Subtract

12.

n²⋅n⁴

a)

n²

b)

n⁸

c)

n⁶

d)

n²²

13.

Which is the simplified form of $3x^2y\ \times\ 5xy$ ?

a)

$15x^2y^{2\ }$

b)

$15x^2y$

c)

$15x^3y$

d)

$15x^{3\ }y^{2\ }$

14.

Which is the simplified form of $g\cdot g^{4\ }\cdot g^3$

a)

$g^7$

b)

$g^8$

c)

$g^{12}$

d)

$g^{13}$

15.

According to the laws of exponents, when dividing keep the base and __________ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

16.

$\frac{\ \ \ x^{15}\ \ \ }{y^{12}}$

a)

$xy^3$

b)

$x^{27}$

c)

Not like bases, laws of exponents can not be applied

d)

$y^3$

17.

Evaluate this expression using the quotient rule.

a)

9⁵

b)

9⁹

c)

1⁵

d)

9^-5

18.

$\frac{18x^{10}}{2x^3}$ Don't panic! Divide the numbers, and then look at the x terms.

a)

$9x^7$

b)

$9x^{13}$

c)

$18x^7$

d)

$2x^{13}$

19.

(x¹⁴)³

a)

x¹⁷

b)

x⁴²

c)

x¹¹

d)

3x¹⁴

20.

Simplify:
(xy²)⁴

a)

x⁴y²

b)

x⁴y⁸

c)

x³y²

d)

x⁵y⁶

21.

Simplify: (3x²)³

a)

27x⁶

b)

9x⁶

c)

3x⁶

d)

9x⁵

22.

Simplify

a)

2b²

b)

2b⁶

c)

6b⁶

d)

8b⁶

23.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

This cannot be determined.

24.

Simplify (-4x)⁰

a)

-4

b)

-4x

c)

-1

d)

1

e)

0

25.

Simplify.
xy⁰

a)

xy

b)

x

c)

1

d)

0

26.

$2^0+\left(3x\right)^0+3^2$

a)

1

b)

11

c)

2

d)

9

27.

Write this expression using positive exponent:

x^-7

a)

-7

b)

-7x

c)

1/x⁷

d)

-1/x⁷

28.

Simplify.
s^-5⋅ s^-2

a)

s^-3

b)

¹/_s⁷

c)

s^-7

d)

¹/_s³

29.

Simplify.

a)

y⁶⁰

b)

¹/_y¹⁶

c)

y^-16

d)

y⁴

30.

Simplify the following expression:
xy^-7

a)

xy⁷

b)

x/y⁷

c)

x⁷/y

d)

x⁷y

31.

Which fraction and decimal are equivalent to 10^-2?

a)

b)

c)

d)

32.

Which exponent will make this statement true?

10^? = 0.000001

a)

6

b)

-6

c)

7

d)

-7

33.

10) What pairs of numbers is equivalent to 10^-5?

a)

b)

c)

d)

34.

What is the smallest power of 10 that exceeds 8,605?

a)

$10^5$

b)

$10^4$

c)

$10^3$

d)

$10^8$

35.

What is the smallest power of 10 that exceeds 345,002?

a)

$10^6$

b)

$10^5$

c)

$10^7$

d)

$10^{10}$

36.

What is the magnitude of

10^{13}

?

a)

10

b)

23

c)

13

d)

130

37.

Write 7.113 x 10⁷ in standard form.

a)

71,130,000

b)

7,113,000

c)

0.0000007113

d)

7,113

38.

Write 6,700 in scientific notation.

a)

6.7 x 10³

b)

6.7 x10^-3

c)

67 x 10²

d)

67 x 10^-2

39.

Write 0.037 in scientific notation.

a)

3.7 x 10^-2

b)

3.7 x 10²

c)

37 x 10^-3

d)

37 x 10³

40.

How would you write 50,000 in scientific notation?

a)

50 x 10⁵

b)

5 x 10⁴

c)

5 x 10³

d)

.5 x 10³

41.

Give the difference of (8.7 x 10⁹) - (2.5 x 10⁷)

a)

6.2 x 10²

b)

6.2 x 10⁹

c)

7.23 x 10⁷

d)

8.675 x 10⁹

42.

Give the difference of (6.4 x 10^-6) - (5.7 x 10^-7)

a)

5.83 x 10^-6

b)

7 x 10^-7

c)

1.23 x 10^-13

d)

1.3 x 10^-6

43.

Give the sum of (2.6 x 10⁶) + (4.2 x 10⁶)

a)

6.8 x 10⁶

b)

6.8 x 10¹²

c)

8.4 x 10⁶

d)

3.2 x 10¹²

44.

Simplify: $\left(5\times10^9\right)+\left(2\times10^6\right)$

a)

$-5.002\times10^9$

b)

$5.002\times10^6$

c)

$-5\times10^{10}$

d)

$5.002\times10^9$

45.

(3.4 x 10⁵)(1.2 x 10^-3)

a)

4.08 x 10^-8

b)

4.8 x 10²

c)

4.08 x 10²

d)

4.08 x 10^-15

46.

(5 x 10⁶)(5 x 10⁷)

a)

2.5 x 10¹²

b)

2.5 x 10¹⁴

c)

25 x 10¹²

d)

25 x 10¹³

47.

Evaluate. Leave your answer in scientific notation.
(9.6×10⁸) ⁄ (3×10⁴)
(hint - it's division...)

a)

6.6×10²

b)

3.2×10¹²

c)

3.2×10⁴

d)

6.6×10⁴

48.

Solve:

(20 x 10⁵⁰) / (4 x 10¹⁵)

a)

2.4 x 10⁵¹

b)

5 x 10⁶⁵

c)

8 x 10⁶⁶

d)

5 x 10³⁵

49.

As part of a community service project, a class planted 7x10⁵ trees in a year. If there are 3.5x10³ students in the school, how many trees did each student plant?

a)

2 x 10⁸

b)

2 x 10²

c)

3.5 x 10⁸

d)

3.5 x 10²

50.

A computer's hard disk drive holds 8 x 10⁷bytes of information. If Jill buys an extra memory stick that holds 3 x 10⁶ bytes of information, how much memory will the computer hold?

a)

11 x 10¹³

b)

11 x 10⁷

c)

8.3 x 10¹³

d)

8.3 x 10⁷

51.

In 1985 Earth had 4.9 ×10⁹ people living on it and in 2005, earth had 6.4 ×10⁹ living on it. How many more people inhabited Earth in 2005 than in 1985?

a)

1.13 x 10⁹

b)

1.13 x 10¹⁰

c)

1.5 x 10⁸

d)

1.5 x 10⁹

52.

The US spends an average of 1.02x10⁴dollars on each student per year. There are about 7.6x10⁷ students in the US. About how much money total is spent on students per year?

a)

7.752 x 10¹¹

b)

7.752 x 10²⁸

c)

8.62 x 10¹¹

d)

8.62 x 10²⁸

53.

Order the following from greatest to least:
5 x 10³
3.2 x 10⁸ 1.2 x 10⁸ 7 x 10⁵

a)

7 x 10⁵ , 5 x 10³ ,
3.2 x 10⁸, 1.2 x 10⁸

b)

3.2 x 10⁸, 1.2 x 10⁸, 7 x 10⁵, 5 x 10³

c)

1.2 x 10⁸, 3.2 x 10⁸,
5 x 10³ , 7 x 10⁵

54.

Which of these numbers is the greatest?

a)

5.406 x 10⁸

b)

5.504 x 10⁷

c)

5.604 x 10⁹

d)

6.504 x 10⁸

55.

Which is the smallest?
1.3 x 10²⁰2.9 x 10²¹9.5 x 10³²8.4 x 10¹⁹

a)

1.3 x 10²⁰

b)

2.9 x 10²¹

c)

9.5 x 10³²

d)

8.4 x 10¹⁹

56.

Which of the following is the GREATEST in value?

a)

9.23 x 10^-2

b)

9.23 x 10^-17

c)

9.23 x 10^-8

d)

9.23 x 10^-5

57.

The table shows the mass in grams of one atom of each of several elements. List the elements in order from the least mass to greatest mass per atom.

a)

hydrogen, carbon, oxygen, silver, gold

b)

hydrogen, oxygen, gold, siver, carbon

c)

carbon, oxygen, silver, gold, hydrogen

d)

gold, oxygen, carbon, silver, hydrogen

58.

Simplify.
(x³ ⋅ y⁴ ⋅ z)³ ⋅ (x⁵ ⋅ y ⋅ z³)²

a)

x¹⁹y¹²z⁹

b)

x¹⁹ y¹⁴z⁹

c)

x¹³y¹⁰z⁹

d)

x²³y⁴²z¹¹

59.

$\frac{-72x^4y^3}{9xy^2}$

a)

$8x^3y$

b)

$-8x^3y$

c)

$-8x^3y^{-1}$

d)

$-8x^2y$

60.

$\frac{42a^2b^2}{-6ab}$

a)

$-7ab$

b)

$-7ab^2$

c)

$7ab$

d)

$-7a^2b^2$

61.

Simplify: $\frac{\left(a^2\cdot6b^{-4}\right)^3}{\left(a^{-1}\right)^{-1}}$

a)

$\frac{216a^5}{b^{12}}$

b)

$\frac{6a^6}{ab^{12}}$

c)

$\frac{6a^5b^{-12}}{a}$

62.

$\frac{-18x^3y^{-9}}{3x^2y^2}$

a)

$\frac{6x}{y^{11}}$

b)

$-\frac{6}{xy^{11}}$

c)

$-\frac{6x}{y^{11}}$

d)

$-\frac{6x}{y^7}$

63.

$\frac{c^{-19}a^{-3}b^{4^{2^2}}c^{20}}{\frac{a^3}{a^{-3}}b^{2^{\left(2^3-1\right)}}}$ (yes really)

a)

no

b)

$\frac{a^9b^{256}}{c^{20}}$

c)

$\frac{b^{128}c}{a^9}$

d)

no thank you i'd rather not

64.

a³b(ab)²

a)

a⁵b³

b)

a⁶b⁴

c)

a²b²

d)

a⁹b⁶

Module 1 Cumulative Review: Eureka Math 8

Total questions: 64

Worksheet time: 3hrs 10mins

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