Free Printable Multiplying Exponents (including negative exponents)

1.

Simplify:
s^-5⋅ s^-2

a)

s^-3

b)

¹/_s⁷

c)

s^-7

d)

¹/_s³

2.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

3.

What is $5^{-4}$ written with a positive exponent?

a)

20

b)

$5^4$

c)

$\frac{1}{5^4}$

d)

-20

4.

What is the value of $3^{-2}$

a)

$\frac{1}{6}$

b)

$\frac{1}{9}$

c)

-9

d)

-6

5.

Rewrite each expression with a negative exponent.
¹/_(-5)⁷

a)

(-5)⁷

b)

¹/_(-5)^-7

c)

(-5)^-7

d)

¹/_78,125

6.

Write with positive exponents:

a)

a^-2

b)

a²

c)

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

d)

2a

7.

Rewrite the following expression using a positive exponent: $g^{-7}$

a)

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

b)

$g^7$

c)

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

d)

$-g^7$

8.

Simplify the following expression: $\frac{1}{x^{-7}}$

a)

$x^7$

b)

$7x$

c)

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

d)

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

9.

10.

Match the following:

a)

$\frac{a^{-3}b^{-5}}{c^{-1}}$

1.

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

b)

$\frac{a^3c^{-1}}{b^{-5}}$

2.

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

c)

$a^{-3}b^{-5}c^{-1}$

3.

$\frac{1}{a^3b^5c}$

d)

$\frac{a^3b^5}{c^{-1}}$

4.

$a^3b^5c$

e)

$\frac{1}{a^{-3}b^5c^{-1}}$

5.

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

11.

$\left(a^{-3}b^4c\right)^{-2}$

a)

$\frac{c^2}{a^6b^8}$

b)

$\frac{b^8}{a^6c^2}$

c)

$\frac{a^6}{b^8c^2}$

12.

$x^9\cdot x^{-7}\cdot x^{-10}$

a)

$x^8$

b)

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

c)

$x^{26}$

d)

$\frac{1}{x^{26}}$

13.

$6g^{-3}\cdot2g^8$

a)

$\frac{12}{g^3}$

b)

$\frac{12}{g^5}$

c)

$12g^5$

d)

$12g^{11}$

14.

$\left(j^{-1}k\right)^{-3}\cdot\left(j^{-5}k^4\right)^2$

a)

$\frac{k^5}{j^7}$

b)

$\frac{j^7}{k^5}$

c)

$j^{13}k^{11}$

d)

$j^7k^5$

15.

$y^4\cdot y^{-4}$

a)

$1$

b)

$0$

c)

$y^8$

d)

$y^{16}$

16.

$\left(\frac{x^{-4}y^6}{z^2}\right)^{-3}$

a)

$\frac{x^{12}z^6}{y^{18}}$

b)

$\frac{y^{18}}{x^{12}z^6}$

c)

$\frac{z^6}{x^{12}y^{18}}$

d)

$\frac{x^{12}}{z^6y^{18}}$

17.

Simplify. Hint: do product rule first, then negative rule!

a)

$42x^5$

b)

$\frac{42}{x^5}$

c)

$\frac{42}{x^{-5}}$

d)

$\frac{1}{42x^5}$

18.

Select ALL solutions that are equivalent to the following expression

a)

1/j³

b)

j^-23

c)

1/j²³

d)

j^-3

19.

Simplify the following
(no negative exponents):

$\left(x^4\right)^{-3}\cdot2x^4$

a)

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

b)

$\frac{2^4}{x^8}$

c)

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

d)

$2x^{-12}x^4$

20.

Simplify the following
(no negative exponents):
$4a^3b^2\cdot3a^{-4}b^{-3}$

a)

$7a^{-1}b^{-1}$

b)

$\frac{12}{ab}$

c)

$12ab$

d)

$\frac{12}{a^{12}b^6}$

21.

$5ay^{-3}$

a)

$\frac{5a}{y^3}$

b)

$\frac{5}{ay^3}$

c)

$\frac{1}{5ay^3}$

d)

$-5ay^3$

22.

$6y^{-2}z^2$

a)

$\frac{1}{6y^2z^2}$

b)

$6y^2z^2$

c)

$\frac{z^2}{6y^2}$

d)

$\frac{6z^2}{y^2}$

23.

Simplify using the Laws of Exponents
$7^2\cdot7^{-4}$

a)

$49$

b)

$\frac{1}{49}$

c)

$2,401$

d)

$\frac{1}{2,401}$

24.

Simplify (-9)⁰

a)

-9

b)

-1

c)

1

d)

9

25.

a)

A

b)

B

c)

C

d)

D

26.

Simplify

a)

42x⁵

b)

-42/x⁵

c)

42/x^-⁵

d)

42/x⁵

27.

6m³n³* 8m²n³

a)

48m⁵n⁹

b)

48m⁶n⁶

c)

48m⁵n⁶

d)

none of the above

28.

$x^{-4}\left(y^5\right)\left(x^6\right)\left(y^{-7}\right)$

a)

$x^2y^{-2}$

b)

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

c)

$x^{10}y^{12}$

d)

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

29.

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

a)

$\frac{1x^3}{y^4}$

b)

$\frac{-12x^2}{y^5}$

c)

$\frac{-12x^3}{y^4}$

d)

$-12x^3y^{-4}$

30.

$yx^{\frac{1}{3}}\cdot xy^{\frac{3}{2}}$

a)

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

b)

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

c)

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

d)

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

31.

(34x⁵y⁶z^-7)⁰

a)

34x⁵y⁶ / z⁷

b)

34x⁵y⁶ / x^-7

c)

0

d)

1

32.

$g^3\ \cdot\ g^{-2}$

a)

1

b)

g

c)

$\frac{1}{g}$

d)

$g^5$

33.

$8^{-6\ }\cdot\ 8^9$

a)

$\frac{1}{8^{15}}$

b)

$\frac{1}{8^3}$

c)

$8^{15}$

d)

$8^3$

34.

$n^{-2\ }\cdot\ n^{-3}$

a)

$n^6$

b)

$\frac{1}{n^6}$

c)

$n^{-5}$

d)

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

35.

$10^2$ Identify the exponent

a)

10

b)

2

36.

$10^2$ Identify the base

a)

10

b)

2

37.

$x^9\cdot x^{-7}\cdot x^{-10}$

a)

$x^8$

b)

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

c)

$x^{26}$

d)

$\frac{1}{x^{26}}$

38.

$6g^{-3}\cdot2g^8$

a)

$\frac{12}{g^3}$

b)

$\frac{12}{g^5}$

c)

$12g^5$

d)

$12g^{11}$

39.

When you raise a power to a power, ___________ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

40.

a)

A

b)

B

c)

C

d)

D

41.

a)

A

b)

B

c)

C

d)

D

42.

a)

A

b)

B

c)

C

d)

D

Multiplying Exponents (including negative exponents)

Total questions: 42

Worksheet time: 4hrs 37mins

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