Free Printable Properties of Integer Exponents

1.

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

a)

True

b)

False

2.

Simplify the following expression:

x^5\cdot x^2

a)

$x^{10}$

b)

$x^3$

c)

$x^7$

d)

$x^{2.5}$

3.

Simplify the following expression:

5x^3\cdot2x^3=

a)

$10$

b)

$10x^6$

c)

$7x^6$

d)

$3x^0$

4.

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

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

5.

Simplify the following expression:

\left(7^6\right)^3

a)

$7^{18}$

b)

$7^9$

c)

$7^2$

d)

$7^3$

6.

Simplify the following:

5^{-2}

a)

$-25$

b)

$\frac{1}{25}$

c)

$-\frac{1}{25}$

d)

$-10$

7.

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

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

8.

Simplify the following expression:

$\frac{b^8}{b^4}$

a)

$b^2$

b)

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

c)

$b^{16}$

d)

$b^4$

9.

Simplify the following expression:

$\frac{a^5b^2}{a^2b^4}$

a)

$a^{10}b^8$

b)

$\frac{a^3}{b^2}$

c)

$a^3b^2$

d)

$\frac{a^7}{b^6}$

10.

Simplify the following:

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

a)

$x^7$

b)

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

c)

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

d)

$-x^7$

11.

Simplify the following expression with only positive exponents:

$x^4y^0z^{-1}$

a)

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

b)

$x^4yz$

c)

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

d)

$1$

12.

Simplify the following expression with only positive exponents:

$\frac{x^6y^{-3}}{x^{-4}y^2}$

a)

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

b)

$\frac{x^{10}}{y^5}$

c)

$x^{10}y^5$

d)

$x^2y^5$

13.

Simplify the following expression:

ab^{-3}

a)

$a^3b$

b)

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

c)

$\frac{ab}{3}$

d)

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

14.

Any number raised to the power of zero is always __________ .

a)

0

b)

1

c)

itself

d)

negative

15.

Simplify the following expression:

-4x^0

a)

$-4$

b)

$-4x$

c)

$1$

d)

$-1$

16.

Simplify the following expression as much as possible:

\frac{4^{10}}{4^{10}}\cdot7^0

a)

28

b)

4

c)

0

d)

1

e)

7

17.

Simplify the following expression:

\left(5^2x^3y^5\right)^0

a)

$25x^3y^5$

b)

$0$

c)

$1$

d)

$5xy$

18.

Simplify the following expression:

2^2\cdot\frac{1}{2^5}\cdot2^0

a)

$\frac{1}{8}$

b)

$1$

c)

$2^3$

d)

$0$

e)

$8$

19.

Simplify the following expression:

\frac{7x^8}{28x^3}

a)

$4x^5$

b)

$35x^{11}$

c)

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

d)

$-21x^5$

20.

Simplify the following:

\left(3a^2b^3c^4\right)\left(5a^{-3}b^5c^{-7}\right)

a)

$15a^5b^8c^{11}$

b)

$\frac{2b^8}{ac^3}$

c)

$\frac{8ab^2}{c^3}$

d)

$\frac{15b^8}{ac^3}$

Properties of Integer Exponents

Total questions: 20

Worksheet time: 1hrs 6mins

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