Free Printable Inequalities and Exponents Review

1.

^{Which point is a solution to the system of inequalities?}

a)

(-8,2)

b)

(-2,-5)

c)

(0,6)

d)

(4, 3)

2.

Which inequality is shown in the graph?

a)

y < 2x + 1

b)

y < -2x + 1

c)

y ≤ 2x + 1

d)

y ≤ -2x + 1

3.

What is the inequality symbol for the equation of this boundary line?

a)

less than

b)

less than or equal to

c)

greater than

d)

greater than or equal to

4.

Which system of inequalities is shown?

a)

y ≥ -x - 1
y < x + 4

b)

y < -x - 1
y ≥ x + 4

c)

y > -x - 1
y ≥ x + 4

d)

y > -x - 1
y ≥ x + 3

5.

Is (5, 2) a solution to the system?
2x+4y<20
3x-2y>11

a)

Yes

b)

No

c)

Sometimes

6.

Which is the graph of the system of inequalities?

a)

b)

c)

d)

7.

Identify the graph represented by the following system of inequalities.

2x - y > 4

4x + 2y < 6

a)

b)

c)

8.

3⁻⁴

a)

1 ⁄ 81

b)

-81

c)

81

d)

1 ⁄ 12

9.

2^-1

a)

1/2

b)

1/1

c)

-1/1

d)

-1/2

10.

What is 10⁰equivalent to?

a)

1

b)

10

c)

0

d)

100

11.

Solve (-8)^-2

a)

1/(-8)²

b)

1/8²

c)

1/64

d)

-64

12.

Rewrite using a positive exponent.
2w^-13

a)

-w¹³

b)

2/_w¹³

c)

2/_w^-13

d)

2w¹³

13.

Simplify (34x⁵y⁶z^-7)⁰

a)

34x⁵y⁶ / z⁷

b)

34x⁵y⁶ / x^-7

c)

0

d)

1

14.

Simplify.

a)

y¹⁵

b)

y⁵

c)

y²

d)

2y⁵

15.

Simplify.
s^-5⋅ s^-2

a)

s^-3

b)

¹/_s⁷

c)

s^-7

d)

¹/_s³

16.

What is the value of (-2)^3?

a)

-8

b)

-6

c)

6

d)

8

17.

Simplify (-4r⁵)(2r⁸)

a)

-8r¹³

b)

-2r¹³

c)

-8r⁴⁰

d)

-2y⁴⁰

18.

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

19.

a)

32t¹¹r⁸

b)

32t³⁰r¹⁵

c)

-32t³⁰r¹⁵

d)

-32t¹¹r⁸

20.

Simplify the exponential expression:

a)

10x^-2

b)

2x²

c)

2x¹²

d)

10x¹²

21.

Simplify the exponential expression.

a)

2x⁶y¹²

b)

2x⁵y⁷

c)

8x⁶y¹²

d)

8x⁵y⁷

22.

Simplify
(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

23.

(6x²)(-3x⁵)

a)

18x⁷

b)

-18x⁷

c)

18x⁷

d)

3x⁷

24.

$\frac{9h^6}{3h^3}$

a)

$3h^9$

b)

$3h^{3\ }$

c)

$3h^{18}$

d)

$h^{3\ }$

25.

Simplify: $\left(5a^3b^5\right)\left(-8ab\right)$

a)

$-40a^4b^6$

b)

$-40a^3b^5$

c)

$-40a^2b^4$

d)

$-3ab$

26.

-3xy³ . (4xy)²

a)

-12x³y⁵

b)

-48x²y⁴

c)

-48x³y⁵

d)

-12x²y⁶

27.

$\left(\frac{-8p^{10}}{7r^3}\right)^{^2}$

a)

-64p²⁰/ 49r⁶

b)

64p²⁰/ 49r⁶

c)

-8p²⁰/ 14r⁶

d)

-64p¹²/ 49r⁵

28.

$\frac{\left(5x^2y^5\right)^2\left(3x^4y^2\right)^{ }}{x^5y^5}$

a)

$75x^3y^7$

b)

$25x^{12}y^5$

c)

$15x^7y^3$

d)

$15x^3y^7$

29.

$\frac{8a^4b^{-5}c^{-6}}{2a^3b^{-2}c^3}$

a)

$\frac{4a}{b^3c^9}$

b)

$4ab^3c^9$

c)

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

d)

$\frac{4a}{b^7c^9}$

30.

$\left(16s^4d^{-2}\right)\ \left(0.5\ s^3d\right)^3$

a)

$2s^{13}d$

b)

$\frac{2s^{13}}{d\ ^5}$

c)

$8s^7d$

d)

$2s^{13}d^5$

31.

$Find\ the\ volume\ of\ the\ cube\ with\ a\ side\ of-2a^3b^{-2}c^4$

a)

$\frac{-\ 8a^9c^{12}}{b^6}$

b)

$\frac{8a^9c^{12}}{b^6}$

c)

$\frac{4\ a^6c^8}{b^4}$

d)

$-\ 8\ a^9b^6c^{12}$

32.

$3^{-2}$

a)

$\frac{1}{3^{-2}}$

b)

$3^2$

c)

$\frac{1}{3^2}$

d)

$3\ \frac{1}{2}$

33.

Simplify. $\left(-3x^2y^4\right)^2$

a)

$9x^4y^8$

b)

$-9x^4y^8$

c)

$-6x^4y^6$

d)

$-3x^2y^6$

34.

a)

36/25

b)

25/36

c)

12/10

d)

10/12

35.

a)

m⁴

b)

m⁶

c)

m¹⁰

d)

1/m⁶

36.

a)

x⁷

b)

1/x³

c)

x³

d)

1/x⁷

37.

$\left(\frac{3x^{-3}y^7}{x^6y^{-4}}\right)^{-3}$

a)

$\frac{3x^9}{y^9}$

b)

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

c)

$\frac{x^{24}}{9y^{30}}$

d)

$\frac{x^{27}}{27y^{33}}$

38.

Simplify the following: $\left(\frac{2x^3}{3x}\right)^{-2}$

a)

$\frac{9}{4x^4}$

b)

$\frac{2}{3x^4}$

c)

$\frac{9x^3}{4}$

d)

$\frac{2x^3}{3}$

39.

$7x^2\ \cdot\ 2x^{-3\cdot}\cdot\ x^8$

a)

$9x^7$

b)

$14x^7$

c)

$\frac{9}{x^{48}}$

d)

$\frac{14}{x^{48}}$

40.

$\left(-3ab\right)\left(2a^2\right)^3\left(b^{-4}\right)$

a)

$\frac{-6a^6}{b^3}$

b)

$-6a^7b^3$

c)

$\frac{-24a^6}{b^3}$

d)

$\frac{-24a^7}{b^3}$

41.

$\left(\frac{2x^2}{x^7y}\right)^3$

a)

$\frac{8x^2}{y^3}$

b)

$\frac{8}{x^{15}y^3}$

c)

$\frac{6}{x^4y^3}$

d)

$\frac{6}{x^5y^4}$

42.

$4c^3\ \cdot\ 12c^{-3}$

a)

$16c^0$

b)

$48$

c)

$\frac{48}{c^9}$

d)

$8$

43.

$\left(13x^9\ \cdot\ 12yz^6\right)^0\cdot\ \left(4x^3\right)^{2\ }\cdot\ \left(2x^2\right)^{-1}$

a)

$8x^4$

b)

$8x^2$

c)

$14x^3$

d)

$14x^8$

44.

$\left(-3ab\right)\left(2a^2\right)^3\left(b^{-4}\right)$

a)

$\frac{-6a^6}{b^3}$

b)

$-6a^7b^3$

c)

$\frac{-24a^6}{b^3}$

d)

$\frac{-24a^7}{b^3}$

45.

\left(3x^4y^{-4}\right)^{-2}

a)

$9x^8y^8$

b)

$\frac{y^8}{9x^8}$

c)

$\frac{6x^2}{y^6}$

d)

$6x^2y^6$

46.

a)

b)

c)

d)

47.

a)

2 / x²

b)

-2x²

c)

2x²

d)

2x¹⁴

48.

\left(y^9\right)^{-3}

*Remember to only have positive exponents in your answer.

a)

$y^{-27}$

b)

$y^6$

c)

$\frac{1}{y^{27}}$

d)

$y^{-6}$

49.

$\frac{50r^6n^{-7}}{2n^2r^4\cdot5n^{-3}r}$

Write your answer with only positive exponents.

a)

$\frac{40r^{11}}{n^8}$

b)

$\frac{5}{n^6}$

c)

$\frac{5r}{n^6}$

d)

$25r^2n^{-6}$

50.

$\frac{m^{-6}n^{-3}}{m^{-13}n^{-1}}$

Write your answer with positive exponents only.

a)

$\frac{m^7}{n^2}$

b)

$\frac{n^2}{m^7}$

c)

$m^7n^2$

d)

$m^7n^4$

51.

$\frac{x^{-7}y^8}{x^{-2}y^{-2}}$

a)

$\frac{y^{10}}{x^5}$

b)

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

c)

$x^5y^6$

d)

$\frac{1}{x^5y^6}$

52.

$\frac{3n^{-6}}{3n^5}$

Write your answer with positive exponents only.

a)

$3n$

b)

$\frac{1}{n}$

c)

$n^{11}$

d)

$\frac{1}{n^{11}}$

Inequalities and Exponents Review

Total questions: 52

Worksheet time: 2hrs 58mins

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