Practice Quiz

Multiple Choice
Identify the choice that best completes the statement or answers the question.

Simplify the given expression.

____ 1.
a. c.

b. d.

____ 2.
a. c.

b. d.

Write the given expression in radical form.

____ 3.
a. c.
b. d.

____ 4.
a. c.
b. d.

____ 5.
a. c.
b. d.
____ 6.
a. c.
b. d.

Write the given radical using rational exponents.

____ 7.
a. c.

b. d.

____ 8.
a. c.
b. d.

____ 9.
a. c.

b. d.

____ 10.
a. c.

b. d.

Simplify the given radical expression.

____ 11.
a. c.
b. d.

____ 12.
a. c.
b. d.
____ 13. .
a. c.
b. d.

____ 14. .
a. c.
b. d.

____ 15.

a. c.

b. d.

____ 16.

a. c.

b. d.

____ 17. Write the exponential expression in radical form.

a. c.
b. d.
____ 18. Write the radical expression in exponential form.
a. c.

b. d.

____ 19. Write in simplest form.

a. c.

b. d. none of these

____ 20. What is the value of ?

a. c.

b. d.
Practice Quiz
Answer Section

MULTIPLE CHOICE

1. ANS: C
Write the expression with all positive exponents. Multiply powers by adding the exponents.

Feedback
A Use the product of powers and not the quotient of powers.
B Did you use the correct formula of the product of powers for rational exponents?
C Correct!
D Add only the exponents.

PTS: 1 DIF: Average REF: Page 261

OBJ: 5-7.3 Simplify expressions in exponential or radical form.
NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 TOP: Simplify expressions in exponential or radical form.
KEY: Exponential Expressions | Radical Expressions
2. ANS: C
Write the expression with all positive exponents. Multiply powers by adding the exponents.

Feedback
A Use the correct formula of the Power of a Power for rational exponents.
B Use the Power of a Power Property and not the Product of Powers Property.
C Correct!
D Use the Power of a Power Property and not the Quotient of Powers Property.

PTS: 1 DIF: Average REF: Page 261

OBJ: 5-7.3 Simplify expressions in exponential or radical form.
NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 TOP: Simplify expressions in exponential or radical form.
KEY: Exponential Expressions | Radical Expressions
3. ANS: C
Use the Power of a Power Property, express the power in the simplest form, and then use the definition of

Feedback
A Use the Power of the Power Property before changing expressions with rational
exponents in radical form.
B Use the correct definition of the fractional exponent of a real number.
C Correct!
D Did you check the exponent of the radicand?

PTS: 1 DIF: Basic REF: Page 261

OBJ: 5-7.1 Write expressions with rational exponents in radical form.
NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 TOP: Write expressions with rational exponents in radical form.
KEY: Rational Exponents | Radical Expressions
4. ANS: C
 Use the Power of a Power Property, express the power in the simplest form, and then use the definition of

Feedback
A Use the Power of the Power Property before changing expressions with rational
exponents in radical form.
B Use the correct definition of a fractional exponent of a real number.
C Correct!
D Did you check the exponent of the radicand?

PTS: 1 DIF: Basic REF: Page 261

OBJ: 5-7.1 Write expressions with rational exponents in radical form.
NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 TOP: Write expressions with rational exponents in radical form.
KEY: Rational Exponents | Radical Expressions
5. ANS: A
Use the Power of a Power Property, express the power in the simplest form, and then use the definition of

Feedback
A Correct!
B Use the Power of the Power Property before changing expressions with rational
exponents in radical form.
C Use the correct definition of the fractional exponent of a real number.
D Did you check the exponent of the radicand?

PTS: 1 DIF: Basic REF: Page 261

OBJ: 5-7.1 Write expressions with rational exponents in radical form.
NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 TOP: Write expressions with rational exponents in radical form.
KEY: Rational Exponents | Radical Expressions
6. ANS: A
Use the Power of a Power Property, express the power in the simplest form, and then use the definition of

Feedback
A Correct!
B Did you check the exponent of the radicand?
C Use the Power of the Power Property before changing expressions with rational
exponents in radical form.
D Use the correct definition of a fractional exponent of a real number.

PTS: 1 DIF: Basic REF: Page 261

OBJ: 5-7.1 Write expressions with rational exponents in radical form.
NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2 TOP: Write expressions with rational exponents in radical form.
KEY: Rational Exponents | Radical Expressions
7. ANS: C
 For any real number b and any positive integer n, .

Feedback
A Did you use the correct property of powers?
B Did you apply the property of powers to each term of the radicand?
C Correct!
D Use the definition of b^1/n on each term of the radicand.

PTS: 1 DIF: Average REF: Page 261

OBJ: 5-7.2 Write expressions given in radical form with rational exponents.
NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2
TOP: Write expressions given in radical form with rational exponents.
KEY: Rational Exponents | Radical Expressions
8. ANS: C

For any real number b and any positive integer n, .

Feedback
A Did you apply the property of powers to each term of the radicand?
B Did you use the correct property of powers?
C Correct!
D Use the definition of b^1/n on each term of the radicand.

PTS: 1 DIF: Average REF: Page 261

OBJ: 5-7.2 Write expressions given in radical form with rational exponents.
NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2
TOP: Write expressions given in radical form with rational exponents.
KEY: Rational Exponents | Radical Expressions
9. ANS: A

For any real number b and any positive integer n, .

Feedback
A Correct!
B Did you use the correct property of powers?
C Did you apply the property of powers to each term of the radicand?
D Use the definition of b^1/n on each term of the radicand.

PTS: 1 DIF: Average REF: Page 261

OBJ: 5-7.2 Write expressions given in radical form with rational exponents.
NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2
TOP: Write expressions given in radical form with rational exponents.
KEY: Rational Exponents | Radical Expressions
10. ANS: A

For any real number b and any positive integer n, .

 Feedback
A Correct!
B Use the definition of b^1/n on each term of the radicand.
C Did you use the correct property of powers?
D Did you apply the property of powers to each term of the radicand?

PTS: 1 DIF: Average REF: Page 261

OBJ: 5-7.2 Write expressions given in radical form with rational exponents.
NAT: NA 1 | NA 6 | NA 8 | NA 9 | NA 2
TOP: Write expressions given in radical form with rational exponents.
KEY: Rational Exponents | Radical Expressions
11. ANS: B
Find the principal square root of each term of the radicand.

Feedback
A Apply the principal root according to the sign of the radical.
B Correct!
C Apply the principal square root of each term of the radicand.
D Apply the principal root of the number under the radical sign.

PTS: 1 DIF: Average REF: Page 248 OBJ: 5-5.1 Simplify radicals.
NAT: NA 1 | NA 6 | NA 7 | NA 8 | NA 2 TOP: Simplify radicals.
KEY: Radicals | Simplify Radicals
12. ANS: D
Find the principal square root of each term of the radicand.

Feedback
A Apply the principal square root of each term of the radicand.
B Apply the principal root of the number under the radical sign.
C Apply the principal root according to the sign of the radical.
D Correct!

PTS: 1 DIF: Average REF: Page 248 OBJ: 5-5.1 Simplify radicals.
NAT: NA 1 | NA 6 | NA 7 | NA 8 | NA 2 TOP: Simplify radicals.
KEY: Radicals | Simplify Radicals
13. ANS: D
Factor into squares where possible. Use the Product Property of Radicals to simplify.

Feedback
A Did you use the Product Property of Radicals?
B Write all the terms left in the radicand also.
C Factor terms in the radicand into squares if possible and then use the Product Property
of Radicals.
D Correct!

PTS: 1 DIF: Average REF: Page 254

OBJ: 5-6.1 Simplify radical expressions using multiplication. NAT: NA 1 | NA 7 | NA 9 | NA 10 | NA 2
TOP: Simplify radical expressions using multiplication.
KEY: Radical Expressions | Simplify Radical Expressions
14. ANS: B
Factor into squares where possible. Use the Product Property of Radicals to simplify.

Feedback
A Did you use the Product Property of Radicals?
B Correct!
C Write all the terms left in the radicand also.
D Factor terms in the radicand into squares if possible and then use the Product Property
of Radicals.

PTS: 1 DIF: Average REF: Page 254

OBJ: 5-6.1 Simplify radical expressions using multiplication. NAT: NA 1 | NA 7 | NA 9 | NA 10 | NA 2
TOP: Simplify radical expressions using multiplication.
KEY: Radical Expressions | Simplify Radical Expressions
15. ANS: B PTS: 1 OBJ: Expressions and Operations
TOP: Write radical expression as expression containing rational exponents
16. ANS: D PTS: 1 OBJ: Expressions and Operations
TOP: Write radical expression as expression containing rational exponents
17. ANS: A PTS: 1 DIF: L1 REF: 7-4 Rational Exponents
OBJ: 7-4.1 Simplifying Expressions with Rational Exponents
NAT: NAEP A3b | CAT5.LV21/22.50 | CAT5.LV21/22.51 | IT.LV17/18.AM | IT.LV17/18.CP | S9.TSK3.NS |
S9.TSK3.PRA | S10.TSK3.NS | S10.TSK3.PRA | TV.LV21/22.10 | TV.LV21/22.12 | TV.LV21/22.52 |
TV.LVALG.53 TOP: 7-4 Example 2
KEY: rational exponent | radical form
MSC: NAEP A3b | CAT5.LV21/22.50 | CAT5.LV21/22.51 | IT.LV17/18.AM | IT.LV17/18.CP | S9.TSK3.NS |
S9.TSK3.PRA | S10.TSK3.NS | S10.TSK3.PRA | TV.LV21/22.10 | TV.LV21/22.12 | TV.LV21/22.52 |
TV.LVALG.53
18. ANS: C PTS: 1 DIF: L3 REF: 7-4 Rational Exponents
OBJ: 7-4.1 Simplifying Expressions with Rational Exponents
NAT: NAEP A3b | CAT5.LV21/22.50 | CAT5.LV21/22.51 | IT.LV17/18.AM | IT.LV17/18.CP | S9.TSK3.NS |
S9.TSK3.PRA | S10.TSK3.NS | S10.TSK3.PRA | TV.LV21/22.10 | TV.LV21/22.12 | TV.LV21/22.52 |
TV.LVALG.53 TOP: 7-4 Example 2
KEY: rational exponent | radical form
MSC: NAEP A3b | CAT5.LV21/22.50 | CAT5.LV21/22.51 | IT.LV17/18.AM | IT.LV17/18.CP | S9.TSK3.NS |
S9.TSK3.PRA | S10.TSK3.NS | S10.TSK3.PRA | TV.LV21/22.10 | TV.LV21/22.12 | TV.LV21/22.52 |
TV.LVALG.53
19. ANS: A PTS: 1 DIF: L1 REF: 7-4 Rational Exponents
OBJ: 7-4.1 Simplifying Expressions with Rational Exponents
NAT: NAEP A3b | CAT5.LV21/22.50 | CAT5.LV21/22.51 | IT.LV17/18.AM | IT.LV17/18.CP | S9.TSK3.NS |
S9.TSK3.PRA | S10.TSK3.NS | S10.TSK3.PRA | TV.LV21/22.10 | TV.LV21/22.12 | TV.LV21/22.52 |
TV.LVALG.53 TOP: 7-4 Example 5
KEY: rational exponent
MSC: NAEP A3b | CAT5.LV21/22.50 | CAT5.LV21/22.51 | IT.LV17/18.AM | IT.LV17/18.CP | S9.TSK3.NS |
S9.TSK3.PRA | S10.TSK3.NS | S10.TSK3.PRA | TV.LV21/22.10 | TV.LV21/22.12 | TV.LV21/22.52 |
TV.LVALG.53
20. ANS: C PTS: 1 REF: York County 2012-2013
OBJ: Expressions and Operations