Free Printable 4.1,4.2,4.5 practice

1.

√98a²⁰c¹⁵

a)

7c√a¹⁰c⁷

b)

7a¹⁰c⁷√2

c)

49a¹⁰c⁷√2c

d)

7a¹⁰c⁷√2c

2.

Simplify the expression

a)

6a⁵b³√6b

b)

2a⁵b³√54b

c)

3a⁵b³

d)

6√2a¹⁰b⁷

3.

Simplify completely:

a)

b)

c)

d)

Cannot be simplified.

4.

a)

A

b)

B

c)

C

d)

D

5.

Simplify $-3\sqrt{3}+\sqrt{27}$

a)

$-4\sqrt{3}$

b)

$2\sqrt{7}$

c)

$24\sqrt{3}$

d)

$0$

6.

What should you multiply $\frac{6}{1-\sqrt{5}}$ by to rationalize the denominator?

a)

-4

b)

$1-\sqrt{5}$

c)

$1+\sqrt{5}$

d)

$-\frac{\left(3-3\sqrt{5}\right)}{2}$

7.

What should you multiply $\frac{3\sqrt{2}}{2-\sqrt{7}}$ by to rationalize the denominator?

a)

$2-\sqrt{7}$

b)

$\sqrt{7}$

c)

$2+\sqrt{7}$

d)

$\sqrt{2}$

8.

Multiply the radical expressions and simplify the result.

$\sqrt[]{5}\cdot\sqrt[]{10}$

a)

$\sqrt[]{50}$

b)

$2\sqrt[]{5}$

c)

$5\sqrt[]{2}$

d)

50

9.

SImplify:

a)

5√6

b)

25√6

c)

√150

d)

10√15

10.

Simplify: $\sqrt[]{\frac{72}{6}}$

a)

$\frac{\sqrt[]{72}}{\sqrt[]{6}}$

b)

$\sqrt[]{12}$

c)

$3\sqrt[]{2}$

d)

$2\ \sqrt[]{3}$

11.

Solve: $\frac{\sqrt[3]{343}}{\sqrt[3]{125}}$

a)

$\frac{7}{5}$

b)

$\frac{5\sqrt[]{2}}{3}$

c)

$7\sqrt[2]{2}$

d)

$\frac{5}{7}$

12.

Rationalize the denominator.
$\frac{\sqrt{120x^6y^2}}{\sqrt{3xy^8}}$

a)

$\frac{2x^3y\sqrt{30}}{y^4\sqrt{3x}}$

b)

$\frac{2x^3\sqrt{30}}{y^4\sqrt{3x}}$

c)

$\frac{2x^2\sqrt{10x}}{y^3}$

d)

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

13.

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

a)

$b^1$

b)

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

c)

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

14.

identify the correct property $\sqrt[3]{b^2}$

a)

$b^1$

b)

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

c)

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

15.

identify the correct property $\frac{\sqrt[3]{b}}{\sqrt[3]{a}}$

a)

$\sqrt[3]{\frac{b}{a}}$

b)

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

c)

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

16.

identify the correct property $\sqrt[7]{b^7}$

a)

$b^{ }$

b)

$b^0$

c)

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

17.

$\sqrt[4]{b}\cdot\sqrt[4]{c}$

a)

$b\cdot c$

b)

$\sqrt[4]{b\cdot c}$

c)

$\sqrt[4]{b-c}$

18.

Simplify the expression:
c⁴⋅c³=

a)

$C^{12}$

b)

c⁴²

c)

c⁷

19.

identify the correct property $4^{3+9}=$

a)

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

b)

$\left(4\right)^{27}$

c)

$4^3\cdot4^9$

d)

$\left(4^3\right)^9$

20.

identify the correct property $\left(4^3\right)^2=$

a)

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

b)

$\left(4\right)^6$

c)

$4^3\cdot4^2$

d)

$4^5$

21.

identify the correct property $\frac{a^3}{a^2}=$

a)

$a^{3-2}$

b)

$a^6$

c)

$a^{-1}$

d)

$a^5$

22.

identify the correct property $\frac{a^4}{b^4}=$

a)

$ab^0$

b)

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

c)

$ab^{4-4}$

d)

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

23.

identify the correct property $a^{2-6}=$

a)

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

b)

$\frac{1}{3}$

c)

$a^{\frac{2}{6}}$

d)

$a^4$

24.

identify the correct property $b^{-6}=$

a)

$b^6$

b)

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

c)

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

d)

$6^b$

25.

identify the correct property $7^0=$

a)

$0$

b)

$7$

c)

$\frac{1}{7}$

d)

$1$

26.

Rewrite the radical to rational exponent:
Reescribe el radical al exponente racional:
$∛9^5$

a)

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

b)

$9^{\frac{5}{3}}$

c)

$9^{\frac{3}{5}}$

d)

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

27.

Rewrite the following as a radical. Simplify if possible.

a)

A

b)

B

c)

C

d)

D

28.

$\left(x^2y^3\right)\left(x^4y^4\right)$

a)

$2x2y$

b)

$x^2y$

c)

$x^6y^7$

d)

$4x12y$

29.

a)

8x⁴

b)

8x⁸

c)

6x⁴

d)

6x⁸

30.

a)

1/p²

b)

p⁴

c)

1/p⁴

d)

p

31.

Simplify $\left(3yx^{-4}\right)^4$

a)

$9x^6y^4$

b)

$\frac{9y^6}{x^6}$

c)

$x^{12}y^8$

d)

$\frac{81y^4}{x^{16}}$

32.

Simplify the expression: $\left(\frac{a^3}{2b^5}\right)^4$

a)

$\frac{a^{12}}{2b^{20}}$

b)

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

c)

$\frac{a^{12}}{16b^{20}}$

d)

$\frac{a^7}{16b^9}$

33.

What is the coefficient for this expression?

$\left(\frac{9x^8y^4}{18x^{10}y^3}\right)^3$

(a)

34.

$\left(10x^9y^2\right)\left(2x^4y^4\right)^3$

Simplify the expression and determine the power on the x.

(a)

35.

a)

2a²b⁶

b)

1/2a²b⁶

c)

b⁶/2a²

d)

2b⁶/a²

36.

a)

b)

c)

d)

37.

(34x⁵y⁶z^-7)⁰

a)

34x⁵y⁶ / z⁷

b)

34x⁵y⁶ / x^-7

c)

0

d)

1

38.

Simplify the expression.
(m⁸k³)/(m⁶k²)

a)

m²k

b)

1/(m²k)

c)

m²/k

d)

k/m²

39.

Use ^ for all exponents! Do not use the space bar!

Show your work on paper!

(a)

40.

Use ^ for all exponents! Use the / symbol for fraction if needed!

Do not use the space bar!

(a)

41.

A piggy bank contains only nickels, dimes and quarters. Given the following information determine the equations that will help you to find how many of each type of coin are in the bank. If

• The coins total $4.50.

• There are 32 coins in the bank.

• The number of nickels and dimes together is 8 more than the number of quarters

a)

0.08n + 0.12d + 0.26q = 4.50

n + d + q = 32

n + d - q = 8

b)

0.05n + 0.10d + 0.25q = 4.50

n + d + q = 32

n + d - q = 8

c)

0.05n + 0.10d + 0.25q = 4.50

n + d + q = 32

n + d +q = 8

42.

The local rodeo sells three types of tickets: general admission cost $49, VIP tickets cost $89 and senior citizen tickets cost $39. On Friday, the rodeo sold a total of 1,500 tickets. Sales totaled $80,600. How many of each type of ticket was sold if 100 more senior citizen tickets were sold than VIP tickets?

a)

General 860

VIP 270

Senior Citizen 370

b)

General 660

VIP 370

Senior Citizen 470

c)

General 1000

VIP 200

Senior Citizen 300

d)

General 860

VIP 370

Senior Citizen 270

43.

The school PALS group sold 255 flowers for Valentine's Day. They sold roses at $2 each, daisies at $1 each and lilies at $1.50 each. They sold twice as many roses as lilies. Total sales came to $405. How many of each type of flower was ordered?

a)

120 Roses

75 Daisies

60 Lilies

b)

60 Roses

75 Daisies

120 Lilies

c)

75 Roses

60 Daisies

120 Lilies

d)

100 Roses

70 Daisies

65 Lilies

44.

Coach Anthony has a jar full of change. There are 37 nickels, dimes, and quarters. The total of the coins is $3.75. If there are twice as many nickels than dimes, how many of each does he have?

a)

20 dimes, 10 nickels, 7 quarters

b)

10 dimes, 20 nickels, 7 quarters

c)

9 dimes, 18 nickels, 10 quarters

45.

Mallory spent $320 on jeans, leggings, and shorts. The jeans were $55, leggings were $15, and the shorts were on sale for $20. She bought one less pair of shorts than leggings. If there were a total of 12 items, how many of each did she buy?

a)

5 jeans, 4 leggings, and 3 shorts

b)

3 jeans, 5 leggings, and 4 shorts

c)

7 jeans, 3 leggings, and 2 shorts

4.1,4.2,4.5 practice

Total questions: 45

Worksheet time: 2hrs 7mins

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