Free Printable Exponent Rules (Product and Quotient)

1.

True or False:

a)

True

b)

False

2.

Simplify the expression.

a)

1²²

b)

1³⁰

c)

6²²

d)

6³⁰

3.

True or False?

a)

True

b)

False

4.

Simplify (c⁵)(c³)(c³)

a)

c⁴⁵

b)

3c¹¹

c)

c¹¹

d)

3c⁴⁵

5.

Evaluate the expression using the quotient rule.

a)

2¹⁴ z¹³

b)

2²/z⁷

c)

2¹⁴/ z⁷

d)

2²z⁷

6.

According to exponent rules, when we multiply two powers with the same base we _______ the exponents.

Example: c⁶ ⋅ c⁴

a)

add

b)

subtract

c)

multiply

d)

divide

7.

According to exponent rules, when we divide two powers with the same base we _______ the exponents.
Example: h⁸/h³

a)

add

b)

subtract

c)

multiply

d)

divide

8.

12h⁸÷ 3h⁴

a)

4h¹²

b)

9h⁴

c)

4h⁴

d)

9h¹²

9.

Rewrite the expression as a power.

(2⁴)(2⁵)

a)

2²⁰

b)

4⁹

c)

4²⁰

d)

2⁹

10.

Simplify: (5p⁹q³)(2pq⁷)

a)

7p¹⁰q¹⁰

b)

10p⁹q²¹

c)

10p¹⁰q¹⁰

d)

10p⁸q^-4

11.

Simplify:

a)

4p³

b)

3p³

c)

1/3p⁴

d)

3p⁴

12.

Simplify: $x^4\cdot x^9$

a)

$x^{13}$

b)

$x^{36}$

c)

$x^5$

d)

$x^2$

13.

Simplify: $y^2\cdot y^6$

a)

$y^{12}$

b)

$y^4$

c)

$y^8$

d)

$y^{26}$

14.

Simplify: $w^9\cdot w^{ }$

a)

$w^9$

b)

$w^{10}$

c)

$w$

d)

$w^8$

15.

Simplify: $\frac{x^9}{x^2}$

a)

$x^{11}$

b)

$x^7$

c)

$x^{18}$

d)

$x^{92}$

16.

Simplify: $x^7\cdot x^5\cdot x^2$

a)

$x^{14}$

b)

$x^{12}$

c)

$x^{70}$

d)

$x^{15}$

17.

Simplify: $h^3\cdot g^2\cdot h^5$

a)

$g^2\cdot h^8$

b)

$gh^{10}$

c)

$g^2\cdot h^{15}$

d)

$h^8$

18.

Simplify: $\left(-2\right)^5\cdot\left(-2\right)^{10}$

a)

$\left(-2\right)^{50}$

b)

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

c)

$2^{15}$

d)

$\left(-2\right)^{15}$

19.

Simplify: $2x^5\cdot5x^6$

a)

$25x^{11}$

b)

$10x^{11}$

c)

$7x^{11}$

d)

$10x^{30}$

20.

Simplify: $\frac{n^5}{n}$

a)

$n^4$

b)

$n^5$

c)

$n^6$

d)

$m^4$

21.

Simplify: $m^5n^9\cdot m^2n^3$

a)

$m^{10}n^{12}$

b)

$m^7n^{27}$

c)

$m^7n^{12}$

d)

$m^{12}n^{27}$

22.

Simplify: $\frac{x^2y^8}{xy}$

a)

$xy^7$

b)

$xy$

c)

$x^3y^9$

d)

$x^3y^7$

23.

Simplify: $\frac{a^{17}b^{10}}{a^2b^7}$

a)

$a^{34}b^{70}$

b)

$a^{15}b^{17}$

c)

$a^{19}b^3$

d)

$a^{15}b^3$

24.

Simplify: $a^2b\cdot a^6b$

a)

$a^8b$

b)

$a^8b^2$

c)

$a^{12}b$

d)

$a^8b^3$

25.

Simplify: $\frac{x^8y^4}{x^2}$

a)

$x^{10}y^4$

b)

$x^{16}y^4$

c)

$x^6y^4$

d)

$x^6y^2$

26.

Simplify: $x^8y^2z^2\cdot xyz$

a)

$x^8y^2z^2$

b)

$x^{9^{ }}y^3z^3$

c)

$xyz^{12}$

d)

$xyz^{15}$

27.

Simplify: $\frac{x^{100}y^{50}}{xy}$

a)

$x^{99}y^{49}$

b)

$x^{101}y^{51}$

c)

$x^{100}y^{50}$

d)

$xy^{150}$

28.

Simplify: $\frac{a^{14}b^4c^5}{a^4b^2c^3}$

a)

$a^{18}b^6c^8$

b)

$a^{14}b^4c^5$

c)

$a^{10}b^2c^2$

d)

$a^{13}b^3c^4$

29.

Simplify the following expression:

x¹⁰ ÷ x²

a)

x⁵

b)

x¹²

c)

x⁸

d)

x²⁰

30.

Simplify

(45x⁶y⁹) ÷ (5x⁴y²)

a)

9x²y⁷

b)

40x²y⁷

c)

9x²/y⁷

d)

9x¹⁰y¹¹

Exponent Rules (Product and Quotient)

Total questions: 30

Worksheet time: 36mins

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