Free Printable Quotient Rule of Exponents

1.

Evaluate this expression using the quotient rule.

a)

9⁵

b)

9⁹

c)

1⁵

d)

9^-5

2.

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

3.

Simplify the exponential expression:

a)

10x^-2

b)

2x²

c)

2x¹²

d)

10x¹²

4.

$\frac{15^9}{15^3}$

a)

15⁶

b)

15¹²

c)

1⁶

d)

1¹²

5.

Simplify the expression.

a)

y¹⁵

b)

y⁵⁰

c)

y²

d)

y⁵

6.

$\frac{x^5y^4z^3}{x^5y^6z^2}$ Simplify

a)

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

b)

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

c)

$y^2z$

d)

$x^{10}y^{10}z^5$

7.

Simplify

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

a)

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

b)

$x^4y^5$

c)

$x^2y^3$

d)

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

8.

Simplify

$\frac{a^5b^7c}{a^9b^5c^2}$

a)

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

b)

$a^4b^2c$

c)

$\frac{b^{12}}{a^{14}c^3}$

d)

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

9.

Simplify

$\frac{b^3c^7}{a^4b^4c^4}$

a)

$\frac{c^3}{a^4}$

b)

$\frac{c^3}{a^4b}$

c)

$a^4b^7c^{11}$

d)

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

10.

Simplify the expression.

a)

7⁶

b)

7^-5

c)

1/7⁵

d)

7⁵

11.

$\frac{\ \ \ x^{15}\ \ \ }{y^{12}}$

a)

$xy^3$

b)

$x^{27}$

c)

Not like bases, laws of exponents can not be applied

d)

$y^3$

12.

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

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

13.

x⁶ / x²

a)

x⁴

b)

x¹²

c)

x³

d)

x⁸

14.

8⁷ ⁄ 8²

a)

8⁵

b)

8⁹

c)

8¹⁴

d)

1⁵

15.

a)

8x⁴

b)

8x⁸

c)

6x⁴

d)

6x⁸

16.

Simplify. Express using exponents.

a)

b⁷

b)

b⁸

c)

b¹⁰

d)

b¹⁷

17.

Simplify. Express using exponents.

a)

12x⁶y⁴

b)

12x¹⁰y⁶

c)

22x¹⁰y⁶

d)

12x⁶y⁶

18.

Quotient Rule: For LIKE BASES, keep the base the same and __________exponents.

a)

multiply

b)

add

c)

subtract

d)

divide

19.

Simplify this expression using the quotient rule.

a)

9⁵

b)

9⁹

c)

1⁵

d)

9^-5

20.

Simplify the expression.

a)

7⁶

b)

7^-5

c)

1/7⁵

d)

7⁵

21.

$\frac{w^4y^6x^2}{w^2y^3x}$ Simplify this expression

a)

$w^6y^9x^3$

b)

$w^2y^3x$

c)

4-3-1

d)

wxy

22.

Evaluate the expression using the quotient of powers rule.

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

d)

a⁸b⁷

23.

$\frac{\ \ \ x^{15}\ \ \ }{y^{12}}$

a)

$xy^3$

b)

$x^{27}$

c)

Not like bases, laws of exponents can not be applied

d)

$y^3$

24.

a)

3x^-1y^-5

b)

3x²y

c)

3xy⁵

d)

-3x³y⁷

25.

$\frac{18x^{10}}{2x^3}$ Hint: divide coefficients

a)

$9x^7$

b)

$9x^{13}$

c)

$18x^7$

d)

$2x^{13}$

26.

Simplify $\frac{x^3}{x^5}$ .

a)

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

b)

$x^2$

c)

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

d)

$x^8$

27.

Simplify $\frac{a^3b}{a^6b^2}$ .

a)

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

b)

$a^3b$

c)

$a^9b^3$

d)

$\frac{1}{a^9b^3}$

28.

Simplify $-\frac{10x^4}{15x^2}$ .

a)

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

b)

$-5x^2$

c)

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

d)

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

29.

$\frac{-x^3y^{10}}{-xy^{10}}$ Simplify

a)

$x^2$

b)

$x^2y$

c)

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

d)

$x^4y^{20}$

30.

Simplify. Your answer should only contain positive exponents.

a)

A

b)

B

c)

C

d)

D

Quotient Rule of Exponents

Total questions: 30

Worksheet time: 3hrs 30mins

Similar Resources on Wayground