Free Printable Laws of Exponents Test Review

1.

[(-4)³]²

a)

(-4)⁶

b)

(-4)⁵

c)

(-4)

d)

(-4)⁻¹

2.

Simplify: (x²y³)³

a)

x⁶y⁹

b)

x⁵y⁶

c)

x¹

d)

x⁶y⁶

3.

Simplify: (4x⁵)²

a)

16x¹⁰

b)

8x¹⁰

c)

16x⁷

d)

8x⁷

4.

$\frac{x^3y}{xy^5}$

a)

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

b)

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

c)

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

d)

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

5.

$\frac{18x^{10}}{2x^3}$

a)

$9x^7$

b)

$9x^{13}$

c)

$18x^7$

d)

$2x^{13}$

6.

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

7.

Simplify a⁴(a⁵).

a)

a⁴⁺⁵ = a⁹

b)

a^4-5= a^-1

c)

a⁴⁽⁵⁾= a²⁰

d)

2a⁴⁺⁵ = 2a⁹

8.

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

a)

$12w^{12}v^8$

b)

$3w^{12}v^8$

c)

$3w^5v^5$

d)

$12w^5v^5$

9.

(2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

10.

a)

4⁹

b)

4⁴⁴

c)

4²¹

d)

4¹⁵

11.

a)

25⁶⁰

b)

25¹⁷

c)

5⁶⁰

d)

5¹⁷

12.

$\left(-2x^3y^2\right)\left(5xy^4\right)$

a)

$3x^3y^8$

b)

$3x^4y^6$

c)

$-10x^3y^8$

d)

$-10x^4y^6$

13.

a)

a⁷

b)

a¹⁰

c)

a³

d)

a^-3

14.

Multiply: $-4e^5\cdot2e^8$

a)

-8e⁴⁰

b)

-2e¹³

c)

-8e¹³

d)

-2e⁴⁰

15.

a)

2a⁴b⁴

b)

4a³b⁴

c)

4a⁸b⁵

d)

2a⁴b³

16.

Simplify (c⁵)(c³)(c³)

a)

c⁴⁵

b)

3c¹¹

c)

c¹¹

d)

3c⁴⁵

17.

Simplify the expression.
x⁴ (x¹²)

a)

x³

b)

x⁴⁸

c)

x¹⁶

d)

x⁸

18.

(2ab)³

a)

2³a³b³

b)

2ab³

c)

6a³b³

d)

6ab

19.

(6x²)(-3x⁵)

a)

18x⁷

b)

-18x⁷

c)

18x¹⁰

d)

3x⁷

20.

Simplify the following expression:

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

a)

x³y⁵

b)

x¹²y¹²

c)

x²⁴y¹⁸

d)

x¹⁰⁸y⁴⁵

21.

Simplify the following expression:
$\frac{30y^{12}}{15y^2}$

a)

2y²⁴

b)

2¹⁰

c)

2y¹⁰

d)

2y¹⁴

22.

a)

b)

c)

d)

23.

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

24.

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

a)

$12w^{12}v^8$

b)

$3w^{12}v^8$

c)

$3w^5v^5$

d)

$12w^5v^5$

25.

Simplify (-4r⁵)(2r⁸)

a)

-8r¹³

b)

-2r¹³

c)

-8r⁴⁰

d)

-2y⁴⁰

26.

Simplify the following:
(x²y)⁵

a)

x⁷y⁵

b)

x²y⁵

c)

x¹⁰y⁵

d)

x⁵y⁵

27.

a)

2a⁴b⁴

b)

4a³b⁴

c)

4a⁸b⁵

d)

2a⁴b³

28.

Which expression represents the product of $\left(2x^2y^2\right)\left(3x^3y^3\right)$ ?

a)

$6x^6y^6$

b)

$5x^5y^5$

c)

$5x^6y^6$

d)

$6x^5y^5$

29.

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

a)

$\frac{6x^{15}y^{12}}{9z^6}$

b)

$\frac{8x^8y^7}{27x^5}$

c)

$\frac{8x^{15}y^{12}}{27z^6}$

d)

$\frac{2x^{15}y^{12}}{3z^6}$

30.

$7a^4b\cdot\left(-3a^5b^6\right)^2$

a)

$63a^{40}b^{12}$

b)

$-42a^{40}b^{12}$

c)

$-63a^{14}b^{13}$

d)

$63a^{14}b^{13}$

31.

Simplify the following:
$\left(\frac{3x^3}{5y}\right)^2$

a)

$\frac{9x^6}{25y^2}$

b)

$\frac{9x^3}{25y}$

c)

$\frac{9x^6}{5y}$

32.

Simplify (-5.7)⁰

a)

1

b)

0

c)

-1

d)

-5.7

33.

8⁰ = 0

a)

True

b)

False

34.

Rewrite using a positive exponent.

\frac{1}{x^{-3}}

a)

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

b)

$x^3$

c)

$3x$

d)

$\frac{1}{3x}$

35.

Simplify. Hint: do quotient rule first then negative rule!

\frac{x^3}{x^8}

a)

$x^5$

b)

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

c)

$x^{11}$

36.

Simplify using your exponent rule(s) (5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

37.

Simplify using positive exponents $\frac{10a^{-3}x^5}{5y^2z^{-4}}$

a)

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

b)

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

c)

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

d)

$\frac{5x^5z^4}{10y^2a^3}$

38.

Simplify using positive exponents. $\frac{x^{-8}}{y^{-9}}$

39.

Simplify x²y^-5

a)

1/x²y⁵

b)

x²/y⁵

c)

y⁵/x²

d)

x²/y^-5

40.

Simplify the expression so that it contains only positive exponents.

a)

b)

c)

d)

41.

Simplify the expression so that it contains only positive exponents.

a)

b)

c)

d)

42.

Simplify each expression so that it contains only positive exponents.

a)

b)

c)

d)

43.

Write in simplified exponent form with no negative exponents. $\left(\frac{g^5x^7}{x^{-7}j^9}\right)^0$

a)

$\frac{g^5x^7}{x^{-7}j^9}$

b)

$0$

c)

1

d)

$\frac{g^5x^{14}}{j^9}$

44.

$4c^8d^{-3}\cdot5c^{-5}d^{-1}$

a)

$9c^3d^4$

b)

$\frac{20c^3}{d^4}$

c)

$20c^3d^4$

d)

$\frac{20}{c^3d^4}$

45.

$\frac{56cd}{8c^2d^4}$

a)

$7cd^3$

b)

$\frac{7}{cd^3}$

c)

$48cd^3$

d)

$\frac{48}{cd^3}$

46.

7^-2

a)

49

b)

10/49

c)

-49

d)

1/49

Laws of Exponents Test Review

Total questions: 46

Worksheet time: 3hrs 39mins

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