Free Printable Properties of Exponents Review

1.

Write this expression using positive exponent:

x^-7

a)

$x^7$

b)

$-x^{\frac{1}{7}}$

c)

$\frac{1}{x^7}$

d)

$-\frac{7}{x}$

2.

Simplify (evaluate):
$7^{-2}$

a)

$\frac{1}{7^2}=\frac{1}{14}$

b)

$7^{-2}=\frac{1}{14}$

c)

$7^{-2}=-49$

d)

$\frac{1}{7^2}=\frac{1}{49}$

3.

Rewrite using a positive exponent.

$w^{-13}$

a)

$-w^{13}$

b)

$\frac{1}{w^{13}}$

c)

$\frac{1}{w^{-13}}$

d)

$-13w$

4.

Write with positive exponents:

a)

a^-2

b)

a²

c)

1/a¹

5.

Rewrite using a positive exponent.

$2w^{-13}$

a)

$\frac{w^{13}}{2}$

b)

$\frac{2}{w^{13}}$

c)

$-\frac{2w}{13}$

d)

$\frac{2}{w^{-13}}$

6.

Simplify (34x⁵y⁶z^-7)⁰

a)

34x⁵y⁶ / z⁷

b)

34x⁵y⁶ / x^-7

c)

0

d)

1

7.

$\frac{a^{-5}}{b^8}$

Simplify.

a)

$ab^{13}$

b)

$\frac{1}{a^5b^8}$

c)

$a^8b^5$

d)

$\frac{b^8}{a^5}$

8.

Simplify.

a)

y¹⁵

b)

y⁵

c)

y²

d)

2y⁵

9.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

10.

Simplify

a)

$4x$

b)

$x^4$

c)

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

d)

$\frac{1}{x^{14}}$

11.

Simplify.

a)

y⁶⁰

b)

¹/_y¹⁶

c)

y^-16

d)

y⁴

12.

Simplify

a)

$7ab^2$

b)

$\frac{a^5}{7b^3}$

c)

$7ab^8$

d)

$\frac{7b^3}{a^5}$

13.

$10x^{-3}y^{-2}$

Rewrite using positive exponents.

a)

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

b)

$10xy^6$

c)

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

d)

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

14.

a)

x²y⁴

b)

x³y⁴

c)

x²/y⁴

d)

x²/y⁵

15.

$\frac{xy^{-8}}{4}$

Simplify the expression.

a)

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

b)

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

c)

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

d)

$\frac{xy^8}{-4}$

16.

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

Simplify the expression.

a)

$a^5b^6$

b)

$ab^{11}$

c)

$\frac{1}{a^5b^6}$

d)

none of these

17.

Simplify the expression so that it contains only positive exponents.

a)

b)

c)

d)

18.

Simplify the expression so that it contains only positive exponents.

a)

b)

c)

d)

19.

Simplify the expression so that it contains only positive exponents.

a)

b)

c)

d)

20.

Simplify each expression so that it contains only positive exponents.

a)

b)

c)

d)

21.

a)

$b$

b)

$\frac{1}{b}$

c)

$b^7$

d)

$b^{12}$

22.

$\frac{x^8y^6}{x^9y^2}$

a)

$xy^3$

b)

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

c)

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

d)

$\frac{xy^{14}}{xy^{11}}$

23.

Simplify the exponential expression:

a)

10x^-2

b)

2x²

c)

2x¹²

d)

10x¹²

24.

Simplify
(-7y²)(5y⁴)

a)

-35y⁶

b)

-2y⁶

c)

-35y⁸

d)

-2y⁸

25.

Simplify:

a)

a²

b)

a³

c)

a⁴

d)

a⁵

26.

Simplify:

a)

a

b)

a²

c)

a³

d)

a⁴

27.

Simplify:

a)

a

b)

a²

c)

a³

d)

a⁴

28.

$y^{\frac{1}{2}}x^{\frac{1}{3}}\cdot x^{\frac{1}{3}}y^{\frac{3}{2}}$

a)

$x^{\frac{4}{3}}y^{\frac{5}{2}}$

b)

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

c)

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

d)

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

29.

Simplify . Your answer should contain only positive exponents. $\frac{2x^{\frac{1}{2}}y^{\frac{1}{3}}}{x^{\frac{4}{3}}y^{-\frac{7}{4}}}$

a)

$\frac{y^{\frac{25}{12}}}{x^{\frac{5}{6}}}$

b)

$\frac{x^{\frac{5}{6}}}{y^{\frac{25}{12}}}$

c)

$\frac{2y^{\frac{25}{12}}}{x^{\frac{5}{6}}}$

d)

$\frac{y^{\frac{17}{12}}}{x^{\frac{5}{6}}}$

30.

a)

-30x¹¹

b)

-30x¹⁸

c)

-x¹¹

d)

-x¹⁸

31.

a)

-15x²yz⁴

b)

1

32.

a)

-30a²⁰c

b)

7a¹³b⁵c

c)

7a²⁰c

d)

-30a¹³b⁵c

33.

a)

$\frac{1}{16}$

b)

$\frac{1}{8}$

c)

-16

d)

-8

34.

a)

$\frac{1}{27}$

b)

$\frac{1}{-9}$

c)

27

d)

9

35.

a)

b)

16c³d³

c)

d)

36.

a)

b)

c)

3x⁴y

d)

37.

a)

b)

-7c⁹

c)

d)

38.

a)

x⁷

b)

x¹¹

c)

d)

39.

a)

b)

c)

1

d)

0

40.

a)

b)

z^-11

c)

z

d)

z¹¹

41.

a)

b)

2x²z⁴

c)

3x²y⁵z⁴

d)

42.

a)

3ab⁸c³

b)

c)

d)

2ab⁸c¹¹

43.

a)

b)

-12x²y

c)

d)

-108xy²

44.

a)

b)

c)

d)

45.

a)

$25x^{22}$

b)

$10x^{22}$

c)

$25x^{13}$

d)

$-25x^{22}$

46.

a)

$\frac{27x^{15}z^3}{y^6}$

b)

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

c)

$27x^8yz^4$

d)

$\frac{27x^8z^4}{y}$

47.

a)

$\frac{16x^{16}z^{32}}{y^{28}}$

b)

$\frac{-16x^{16}z^{32}}{y^{28}}$

c)

$\frac{x^{16}z^{32}}{16y^{28}}$

d)

$-8x^{-8}y^3z^{-12}$

48.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

49.

-4x⁰

a)

-4x

b)

-4

c)

1

d)

-1

50.

a)

b)

c)

d)

51.

a)

b)

c)

d)

52.

When dividing powers with the same base, you _______________ the exponents.

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

53.

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

a)

add

b)

subtract

c)

multiply

d)

divide

54.

In order to multiply powers with the same base, we add their exponents.

a)

True

b)

False

55.

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

a)

$x^{12}y^6$

b)

$\frac{x^{12}}{y^{-6}}$

c)

$x^7y$

d)

$\frac{y^6}{x^{12}}$

56.

If the area of a rectangle is $42x^8y^6$ and length is $7x^2y^3$ what is the width?

a)

$6x^4y^2$

b)

$49x^{10}y^9$

c)

$6x^6y^3$

d)

$35x^6y^3$

57.

a)

10t²

b)

10/t²

c)

18t²

d)

2t

58.

Simplify:

a)

x⁶y⁴

b)

x²y⁴

c)

x⁸y⁴

d)

x⁸y

59.

If (2^x)⁵=2¹⁵, what does x equal?

a)

x = 3

b)

x = 5

c)

x = 10

60.

$\left(4x^2\right)^3$ is the same as...

a)

$\left(4\cdot3\cdot x\cdot x\right)\left(4\cdot3\cdot x\cdot x\right)$

b)

$\left(4\cdot x\cdot x\cdot3\right)$

c)

$\left(4\cdot x\cdot x\right)\left(4\cdot x\cdot x\right)\left(4\cdot x\cdot x\right)$

Properties of Exponents Review

Total questions: 60

Worksheet time: 6hrs 34mins

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