Free Printable 2.8 Exponent Practice

1.

$\frac{\left(32w^9v^4\right)}{\left(4wv\right)^2}$

Simplify Using Exponent Rules

a)

$2w^7v^2$

b)

$32w^{11}v^6$

c)

$12w^5v^{12}$

d)

$24w^6v^7$

2.

$\frac{\left(2pq\right)\left(3p^2q^4\right)}{-6pq^5}$

Simplify Using Exponent Rules

a)

$-p^2$

b)

$p^2$

c)

$6p^2$

d)

$12p$

3.

$\frac{\left(8cd^3\right)\left(-3c^4\right)}{6c^2d}$

Simplify Using Exponent Rules

a)

$-4c^3d^2$

b)

$8d^2c^3$

c)

$-12c^6d^4$

d)

$10c^8d^2$

4.

$\frac{\left(8r^5s^2\right)\left(3r^3s^4\right)}{12rs^4}$

Simplify Using Exponent Rules

a)

$2r^7s^2$

b)

$4r^7s^2$

c)

$4r^2s^7$

d)

$10r^7s^2$

5.

$\frac{\left(10ab\right)^2\left(2a^4b^3\right)}{4a^5b}$

Simplify Using Exponent Rules:

a)

$50ab^4$

b)

$25a^7b$

c)

$200a^2b^6$

d)

$25a^{11}b^6$

6.

$\frac{\left(3m^2\right)^2\left(-4n^5\right)^2}{8m^3n^4}$

Simplify Using Exponent Rules:

a)

$18mn^6$

b)

$-12m^7n^{14}$

c)

$144m^{28}n^{40}$

d)

$8m^2n^5$

7.

$\frac{\left(2m^2\right)^3\left(3n^4\right)^3}{9m^4n^7}$

Simplify Using Exponent Rules:

a)

$24m^2n^5$

b)

$-12m^5n^2$

c)

$27m^{10}n^{19}$

d)

$8m^{24}n^{19}$

8.

$\left(\frac{3x^{-3}y^7}{x^6y^{-4}}\right)^{-3}$

a)

$\frac{3x^9}{y^9}$

b)

$\frac{y^{11}}{9x^9}$

c)

$\frac{x^{24}}{9y^{30}}$

d)

$\frac{x^{27}}{27y^{33}}$

9.

Simplify the following: $\left(\frac{2x^3}{3x}\right)^{-2}$

a)

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

b)

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

c)

$\frac{9x^3}{4}$

d)

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

10.

Anything raised to the power of zero is:

a)

positive

b)

negative

c)

0

d)

1

11.

According to exponent rules, when you multiply exponential expressions with the same base, you _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

12.

Simplify: $6m^3\ \cdot\ 8m^4$

a)

$-48m^{12}$

b)

$48m^{12}$

c)

$-48m^7$

d)

$48m^7$

13.

Simplify: $\left(-2k\right)^3$

a)

$-6k^3$

b)

$-8k^3$

c)

$6k^3$

d)

$8k^3$

14.

According to exponent rules, when we raise an exponential expression to a power we ____________ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

15.

The exponent rules state that when exponential expressions with the same base are divided we ______ the exponents.

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

16.

$7x^2\ \cdot\ 2x^{-3\cdot}\cdot\ x^8$

a)

$9x^7$

b)

$14x^7$

c)

$\frac{9}{x^{48}}$

d)

$\frac{14}{x^{48}}$

17.

$\frac{-40x^3y^4}{-8x^3y}$

a)

$5y^3$

b)

$5y^5$

c)

$32y^3$

d)

$32y^5$

18.

Simplify: $2n^4\ \cdot\ \left(n^2\right)^4$

a)

$2n^6$

b)

$2n^8$

c)

$2n^{10}$

d)

$2n^{12}$

19.

Simplify: $4y^4\ \cdot\ 7x^3y^{-2}$

a)

$11x^3y^2$

b)

$\frac{11x^7}{y^2}$

c)

$28x^3y^2$

d)

$\frac{28x}{y^2}$

20.

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

a)

$\frac{-6a^6}{b^3}$

b)

$-6a^7b^3$

c)

$\frac{-24a^6}{b^3}$

d)

$\frac{-24a^7}{b^3}$

21.

$\left(\frac{2x^2}{x^7y}\right)^3$

a)

$\frac{8x^2}{y^3}$

b)

$\frac{8}{x^{15}y^3}$

c)

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

d)

$\frac{6}{x^5y^4}$

22.

Simplify: $\left(-a\right)^3\left(3a^2\right)^2$

a)

$-6a^1$

b)

$-6a^7$

c)

$-9a^7$

d)

$-9a^{10}$

23.

$\frac{\left(k^{-3}\right)^{-8}}{\left(k^8\right)^3}$

a)

$\frac{1}{k^{35}}$

b)

$1$

c)

$k^{13}$

d)

$\frac{1}{k^{22}}$

24.

$4c^3\ \cdot\ 12c^{-3}$

a)

$16c^0$

b)

$48$

c)

$\frac{48}{c^9}$

d)

$8$

25.

$\left(13x^9\ \cdot\ 12yz^6\right)^0\cdot\ \left(4x^3\right)^{2\ }\cdot\ \left(2x^2\right)^{-1}$

a)

$8x^4$

b)

$8x^2$

c)

$14x^3$

d)

$14x^8$

26.

$x^{-5}$ =

a)

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

b)

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

c)

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

d)

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

27.

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

a)

$x^{12\ }$

b)

$x^{-1}$

c)

$x^7$

d)

$x^{34}$

28.

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

a)

$m^8$

b)

$m^{12}$

c)

$m^4$

d)

$m^9$

29.

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

a)

$x^6$

b)

$x^{12}$

c)

$x^{-42}$

d)

$x^{-12}$

30.

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

a)

$x^{13}$

b)

$x^{36}$

c)

$x^5$

d)

$x^{-5}$

31.

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

a)

$x^9$

b)

$x^{25}$

c)

$x^{-9}$

d)

$x^{-25}$

32.

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

a)

$3x^2$

b)

$3x$

c)

$9x$

d)

$6x$

33.

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

a)

$a^8b^{16}$

b)

$a^2b^4$

c)

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

d)

$a^2b^{16}$

34.

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

a)

$x^{14}$

b)

$x^9$

c)

$x^5$

d)

$2x^7$

35.

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

a)

$a^3b^{35}$

b)

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

c)

$a^8b^8$

d)

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

36.

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

a)

$ab^{16}$

b)

$a^8b^{16}$

c)

$a^9b^{10}$

d)

$ab^{10}$

37.

Simplify

x⁻⁶

a)

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

b)

x⁶

c)

-x⁶

d)

$\frac{-1}{x^6}$

38.

Simplify. Hint: do quotient rule first then negative rule!

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

a)

$x^5$

b)

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

c)

$x^{11}$

39.

$5^0\ =\$

a)

1

b)

5

c)

50

d)

0

40.

Simplify the following
(no negative exponents):

$\frac{xy^7}{x^3y^4}$

a)

$x^4y^{11}$

b)

$x^3y^{28}$

c)

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

d)

$\frac{x^4}{y^{11}}$

41.

Simplify:
(x³)²

a)

x⁵

b)

x

c)

x⁶

d)

3x²

42.

Simplify:
(5ab²)²

a)

25a²b⁴

b)

10a²b⁴

c)

5a²b⁴

d)

25ab²

43.

a)

8x⁴

b)

8x⁸

c)

6x⁴

d)

6x⁸

44.

$\frac{\left(2a^2b^4\right)^3}{4a^3b^7}$

Simplify Using Exponent Rules

a)

$2a^3b^5$

b)

$6a^9b^{19}$

c)

$8a^4b^4$

d)

$10a^7b^{12}$

45.

Simplify: 3x³ ⋅ 3x

a)

3²x⁴

b)

3 ⋅ x ⋅ x ⋅ x ⋅3 ⋅ x

c)

9x⁴

d)

3x⁴

46.

Simplify: (6x²)(-3x⁵)

a)

18x⁷

b)

-18x⁷

c)

18x⁷

d)

3x⁷

47.

(x⁵)⁴

a)

x⁹

b)

x²⁰

c)

x

d)

x⁵⁴

48.

(x³y)⁶

a)

2x¹⁸y⁶

b)

x¹⁸y⁶

c)

x³y⁶

d)

x³y⁶

2.8 Exponent Practice

Total questions: 48

Worksheet time: 46mins

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