Free Printable Rules of Exponents

1.

According to exponent rules, when we raise the power to a power we _______ the exponents.
Example: (d²)⁵

a)

add

b)

subtract

c)

multiply

d)

divide

2.

According to exponent rules, when we multiply two power with the same base we _______ the exponents.
Example: c⁶ ⋅ c⁴

a)

add

b)

subtract

c)

multiply

d)

divide

3.

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

4.

$10\times10\times10\times10\times10=$

a)

$10\times5$

b)

$10^5$

5.

$10^3=$

a)

$10\times10\times10$

b)

$10\times3$

c)

$10+10+10$

d)

10,000

6.

Which number is the BASE? $2^7$ =128

a)

2

b)

7

c)

128

d)

$2^7$

7.

If a number or variable does not have an exponent, we can assume the exponent is:

a)

0

b)

1

8.

$y^0=$

a)

y

b)

0

c)

1

d)

10

9.

$365^0=$

a)

0

b)

1

c)

365

d)

$\frac{1}{365}$

10.

$x^{-5}$ =

a)

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

b)

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

c)

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

d)

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

11.

The product rule says that when you are multiplying two exponents with the same base, you keep the base and ________ the exponents

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

12.

$x^3\cdot x^4\ =$

a)

$x^{12\ }$

b)

$x^{-1}$

c)

$x^7$

d)

$x^{34}$

13.

$m^2\cdot m^6\cdot m=$

a)

$m^8$

b)

$m^{12}$

c)

$m^4$

d)

$m^9$

14.

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

a)

$x^6$

b)

$x^{12}$

c)

$x^{-42}$

d)

$x^{-12}$

15.

The quotient rule says that when you are dividing two exponents with the same base, you keep the base and __________ the exponents.

a)

Add

b)

Subract

c)

Multiply

d)

Divide

16.

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

a)

$x^{13}$

b)

$x^{36}$

c)

$x^5$

d)

$x^{-5}$

17.

$\frac{x^{17}}{x^8}$

a)

$x^9$

b)

$x^{25}$

c)

$x^{-9}$

d)

$x^{-25}$

18.

$\frac{9x^2}{3x^{ }}=$

a)

$3x^2$

b)

$3x$

c)

$9x$

d)

$6x$

19.

$\frac{a^5b^{10}}{a^3b^6}=$

a)

$a^8b^{16}$

b)

$a^2b^4$

c)

$a^{15}b^{60}$

d)

$a^2b^{16}$

20.

$\left(x^5\right)^4$

The power of a power rule says that when an exponential expression is raised to a power (as shown above), you should _________ the inner and outer exponents

a)

add

b)

subtract

c)

multiply

d)

divide

21.

$\left(x^7\right)^2$ =

a)

$x^{14}$

b)

$x^9$

c)

$x^5$

d)

$2x^7$

22.

$\left(a^3b^5\right)^7$ =

a)

$a^3b^{35}$

b)

$a^{10}b^{12}$

c)

$a^8b^8$

d)

$a^{21}b^{35}$

23.

$\left(ab^2\right)^8$ =

a)

$ab^{16}$

b)

$a^8b^{16}$

c)

$a^9b^{10}$

d)

$ab^{10}$

24.

Exponent Rules: Product Rule

a^x\cdot a^y=

a)

$a^{x\cdot y}$

b)

$a^{x+y}$

c)

$a^x+a^y$

25.

Exponent Rules: Quotient Rule

\frac{a^x}{a^y}=

a)

$a^{x-y}$

b)

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

c)

$a^{x+y}$

26.

Exponent Rules: Power of a Power Rule

a^{x^y}\ or\ \left(a^x\right)^y\ =

a)

$a^{x+y}$

b)

$a^{x\cdot y}$

c)

$a^xa^y$

27.

Exponent Rules: Negative Exponent

a^{-x}=

a)

$-a^{-x}$

b)

$-a^x$

c)

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

d)

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

28.

Exponent Rules: Power of a Product

\left(ab\right)^x=

a)

$a^x+b^x$

b)

$a^{bx}$

c)

$a^xb^x$

29.

A container of salt contains $5^7$ grains of salt. If a factory has $5^4$ containers inside, how many grains of salt are in the factory?

a)

$5^{11}$

b)

$5^7+5^4$

c)

$5^{28}$

d)

$5^3$

30.

Write each product using an exponent. 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7

a)

7⁷

b)

7⁸

c)

8⁷

d)

7⁹

31.

Simplify the expression: c⁴⋅c³=

a)

^c12

b)

c⁴⁺³

c)

c⁷

32.

(3⁴)(3⁷)

a)

3²⁸

b)

3³

c)

3^-3

d)

3¹¹

33.

Simplify. Your answer should contain only positive exponents. $x^2\cdot x^4$

a)

$x^2$

b)

$x^6$

c)

$x^{-2}$

d)

$x^8$

34.

Simplify the expression: $d^8\cdot d^{10}$

a)

$d^2$

b)

$d^{80}$

c)

$d^{810}$

d)

$d^{18}$

35.

(r⁴)⁶

a)

10r

b)

r¹⁰

c)

24r

d)

r²⁴

36.

(x²)⁶

a)

x¹²

b)

x⁸

c)

x²⁶

d)

x⁴

37.

Evaluate this expression using the quotient rule.

a)

9⁵

b)

9⁹

c)

1⁵

d)

9^-5

38.

How else can you write $\sqrt{x}$ ?

a)

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

b)

$x^2$

c)

$x^{-2}$

d)

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

39.

Which radical expression is equivalent to $x^{\frac{5}{8}}$

a)

$\frac{1}{\sqrt[8]{x}}$

b)

$\sqrt[5]{x^8}$

c)

$\sqrt[\frac{1}{8}]{x}$

d)

$\sqrt[8]{x^5}$

40.

Which exponential expression is equal to $\sqrt[7]{b}$ ?

a)

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

b)

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

c)

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

d)

$b^7$

41.

Which of the following is equivalent to $\sqrt[4]{7^2}$

a)

$\sqrt[4]{14}$

b)

49

c)

$7^{\frac{4}{2}}$

d)

$7^{\frac{2}{4}}$

42.

Which of the following is equivalent to
$156^{\frac{1}{12}}$

a)

$\sqrt[]{156}$

b)

$\frac{156}{12}$

c)

$\sqrt[12]{156}$

d)

12

43.

Which is equivalent to $\sqrt[3]{v}$ ?

a)

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

b)

$v^3$

c)

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

d)

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

44.

How else could you write $4^{-2}$ ?

a)

$16$

b)

$-16$

c)

$-\frac{1}{16}$

d)

$\frac{1}{16}$

45.

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

a)

$\sqrt[3]{x^2}$

b)

$\sqrt[2]{x^3}$

c)

$x^6$

d)

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

Rules of Exponents

Total questions: 45

Worksheet time: 48mins

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