Free Printable Test 8: Exponential Expressions & Equations REVIEW

1.

Simplify (-5.7)⁰

a)

1

b)

0

c)

-1

d)

-5.7

2.

(2x)³

a)

2x³

b)

8x²

c)

8x³

d)

6x³

3.

n²⋅n⁴⋅n⁵

a)

n¹¹

b)

n⁴⁰

c)

n¹³

d)

n²²

4.

Simplify the expression.
1/w^-5

a)

1/w⁵

b)

w⁵

c)

w^-5

d)

1/w^-5

5.

Simplify the expression $\left(2mp\right)^3$

a)

$2mp^3$

b)

$2m^3p^3$

c)

$6m^3p^3$

d)

$8m^3p^3$

6.

Simplify the expression. Only use positive exponents. $a^{-2}b^{-4}$

a)

$a^2b^4$

b)

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

c)

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

d)

$\frac{1}{a^2b^4}$

7.

Simplify the expression:

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

a)

$25xy$

b)

$25xy^2$

c)

$5x^2y^2$

d)

$25x^2y^2$

8.

$\frac{36x^4y^2z}{-6x^4}$

a)

$-6x^0y^2z$

b)

$-6y^2z$

c)

$-6y^3z$

d)

$6y^2z^2$

9.

x⁸ / x²

a)

x⁴

b)

x¹⁶

c)

x^-6

d)

x⁶

10.

a)

−30x¹¹

b)

−30x¹⁸

c)

−x¹¹

d)

−x¹⁸

11.

a)

b⁶

b)

b⁷

c)

b¹

d)

b⁻⁶

12.

a)

a^-3

b)

a³

c)

3a

d)

1/a^-3

13.

a)

b)

c)

d)

14.

a)

a⁶

b)

a^-60

c)

a⁴

d)

a^-7

15.

4x^-2

a)

1/4x²

b)

-4x²

c)

4x

d)

4/x²

16.

Simplify (-9)⁰

a)

-9

b)

-1

c)

1

d)

9

17.

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

a)

$16x^8$

b)

$\frac{1}{16x^8}$

c)

$\frac{1}{2x^8}$

d)

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

18.

Simplify $4a^2b^4\cdot3a^2b^2$

a)

$\frac{4b^3}{a^5}$

b)

$12a^4b^6$

c)

$6b^8a$

d)

$24b$

19.

Simplify $\left(3yx^{-4}\right)^4$

a)

$9x^6y^4$

b)

$\frac{9y^6}{x^6}$

c)

$x^{12}y^8$

d)

$\frac{81y^4}{x^{16}}$

20.

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

a)

add

b)

subtract

c)

multiply

d)

divide

21.

(34x⁵y⁶z^-7)⁰

a)

34x⁵y⁶ / z⁷

b)

34x⁵y⁶ / x^-7

c)

0

d)

1

22.

(-3y^-5)^-2

a)

y¹⁰ / 9

b)

9 / y^-7

c)

6 / y⁷

d)

6 / y³

23.

3x⁻³

a)

1⁄3x³

b)

3⁄x³

c)

3x³

d)

-3x³

24.

What is the value of x?
3^{16 =}(3⁸)(3^x)

a)

2

b)

8

c)

4

d)

1

25.

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

a)

x¹⁹y¹²z⁹

b)

x¹⁹ y¹⁴z⁹

c)

x¹³y¹⁰z⁹

d)

x²³y⁴²z¹¹

26.

A rectangle has an area of 24m² and a base of 4m. What is the height?

a)

20m

b)

6

c)

6m

d)

6m²

27.

Evaluate the expression:

$\left(4x^0y^{-5}\right)^2$

a)

$\frac{16}{y^{10}}$

b)

$16y^{10}$

c)

$\frac{16x}{y^{10}}$

d)

$16xy^{10}$

28.

a)

A

b)

B

c)

C

d)

D

29.

a)

A

b)

B

c)

C

d)

D

30.

a)

A

b)

B

c)

C

d)

D

31.

a)

A

b)

B

c)

C

d)

D

32.

a)

A

b)

B

c)

C

d)

D

33.

a)

A

b)

B

c)

C

d)

D

34.

Simplify the expression

a)

x⁵

b)

1/x⁵

c)

x¹³

d)

1/x¹³

35.

a)

A

b)

B

c)

C

d)

D

36.

Solve for x.

2^x = 4^x+1

a)

x = -2

b)

x = 2

c)

x = -3

d)

x = 3

37.

Sovle for x.

5^{-3x - 1} = 25

a)

x = -1

b)

x = -4

c)

x = -3

d)

x = 1

38.

Solve for x.

3³ = 3^{4x + 2}

a)

x = ¼

b)

x = -¼

c)

x = ½

d)

x = -½

39.

Solve for m.

2^-m = 2^3m-3

a)

4/3

b)

3/4

c)

2

d)

1

40.

Solve for x.

2^x+6 = 32

a)

x=-1

b)

x=11

c)

x=1

d)

x=-11

41.

Solve for p.

4^p+2 = 64

a)

p = 6

b)

p = 1

c)

p = 8

d)

p = 7/6

42.

Solve the following exponential equation.

$2^{3n}=4$

a)

$n=2$

b)

$n=3$

c)

$n=\frac{2}{3}$

d)

$n=4$

43.

Solve the following exponential equation.

$9^{8-x}=27^{x-3}$

a)

$x=5$

b)

$x=-5$

c)

$x=\frac{1}{5}$

d)

$x=-\frac{1}{5}$

44.

Solve for x.

$25^{x+3}=5^{5x-9}$

a)

1

b)

4

c)

5

d)

3

45.

Solve for x.

16^2x = 256^2x+5

a)

5

b)

-5

c)

2

d)

16

46.

Solve for x.

16^x+5 = 64^-2

a)

1/2

b)

8

c)

-8

d)

2

47.

Solve for x.

3^2x+4 = 27^2x-4

a)

4

b)

1/4

c)

-2

d)

-4

48.

Solve for x.

9^8-x = 27^x-3

a)

x = 5

b)

x = -5

c)

x = 1/5

d)

x = -1/5

49.

Solve

a)

-1/3

b)

-3

c)

-1

d)

3

50.

Solve:
5^{1/2x + 4}= 125

a)

1

b)

2

c)

-2

d)

14

51.

Solve:
16^x-3 = 8^x-3

a)

9

b)

-3

c)

0

d)

3

52.

To solve 36 = 6^x, re-write 36 as what base and exponent?

a)

3⁶

b)

6³

c)

6²

d)

3¹²

53.

To solve 8 = 2^5x+7, you would need to re-write 8 as what base?

a)

8

b)

4

c)

2

d)

Cannot be determined

54.

Solve 8 = 2^5x+7

a)

⅘

b)

¼

c)

-⅘

d)

-¼

55.

Solve for n:
2^-2n = 2⁶

a)

-1

b)

-7

c)

5

d)

-3

56.

Solve for p:
4^p+2 = 64

a)

p = -16/9

b)

p = 1

c)

p = 8

d)

p = 7/6

57.

81^3-x = (1/3)^5x-6

a)

6

b)

-6

c)

9/2

d)

3/2

58.

Solve for x:
(1/8)^x = 2³

a)

x=−3

b)

x=3

c)

x=−1

d)

x=1

59.

10^2x+4 =100000

a)

x=7

b)

x=20

c)

x=-1/2

d)

x=1/2

60.

Solve

a)

2

b)

-2

c)

3

d)

-3

61.

Solve

a)

-1/3

b)

-3

c)

-1

d)

3

62.

Solve

a)

-2

b)

6

c)

9

d)

3

63.

When solving exponential equations, you must first get like _______?

a)

exponents

b)

bases

64.

Solve: 7^-x = 49

a)

x = 1

b)

x = -1

c)

x = 2

d)

x = -2

Test 8: Exponential Expressions & Equations REVIEW

Total questions: 64

Worksheet time: 16hrs 0mins

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