What does $$x^{\frac{1}{2}}$$ represent?

It represents the square root of $$x$$ , or @@ oot{2}{x}@@.

Convert $$z^{10}$$ to exponential form with a rational exponent.

$$z^{10} = z^{\frac{10}{1}}$$ .

What is the value of $$x^{\frac{3}{4}}y^2z^{\frac{1}{2}}$$ when $$x=16, y=4, z=9$$ ?

Substituting the values: $$16^{\frac{3}{4}} \times 4^2 \times 9^{\frac{1}{2}} = 8 \times 16 \times 3 = 384$$ .

How do you multiply expressions with rational exponents?

Add the exponents if the bases are the same. For example, $$x^{\frac{1}{2}} \times x^{\frac{1}{3}} = x^{\frac{1}{2} + \frac{1}{3}} = x^{\frac{5}{6}}$$ .

What is the simplified form of $$\frac{x^{\frac{3}{4}}}{x^{\frac{1}{2}}}$$ ?

Subtract the exponents: $$x^{\frac{3}{4} - \frac{1}{2}} = x^{\frac{3}{4} - \frac{2}{4}} = x^{\frac{1}{4}}$$ .

Convert $$x^{\frac{1}{3}}y^{\frac{2}{5}}z^{\frac{1}{10}}$$ to radical form.

@@ oot{3}{x} imes y^{rac{2}{5}} imes oot{10}{z}@@.

What is the value of @@ oot{4}{16}@@?

The value is 2, since $$2^4 = 16$$ .

What is the simplified form of $$x^{\frac{1}{2}} \times x^{\frac{1}{2}}$$ ?

$$x^{\frac{1}{2} + \frac{1}{2}} = x^1 = x$$ .

Honors Rational Exponents Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is a rational exponent?

Back

2.

FLASHCARD QUESTION

Front

Back

@@ oot{4}{x^3}@@

3.

FLASHCARD QUESTION

Front

What is the relationship between rational exponents and roots?

Back

4.

FLASHCARD QUESTION

Front

Back

The expression is already in simplest form.

5.

FLASHCARD QUESTION

Front

Back

@@y^{rac{5}{2}} = y^2 imes oot{2}{y}@@.

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

The expression is already in simplest form.

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

15 questions

Function Operations and Composite Functions

Flashcard

•

9th Grade - University

10 questions

2025 S3/4 CCKS Enzymes

Flashcard

•

8th Grade - University

11 questions

Unit 1 | Topic 2 | Key Terms - Flashcards

Flashcard

•

9th - 12th Grade

15 questions

Unit 4 Test Review

Flashcard

•

10th Grade - University

11 questions

Genetic Engineering Concepts

Flashcard

•

11th Grade - University

8 questions

MAT_8_EF_QN01-QN08

Flashcard

•

8th Grade - University

10 questions

Disney descendants flashcard

Flashcard

•

KG

Popular Resources on Wayground

15 questions

Fractions on a Number Line

Quiz

•

3rd Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

54 questions

Analyzing Line Graphs & Tables

Quiz

•

4th Grade

$fractions$

22 questions

fractions

Quiz

•

3rd Grade

20 questions

Main Idea and Details

Quiz

•

5th Grade

20 questions

Context Clues

Quiz

•

6th Grade

15 questions

Equivalent Fractions

Quiz

•

4th Grade

Discover more resources for Mathematics

20 questions

Graphing Inequalities on a Number Line

Quiz

•

6th - 9th Grade

18 questions

SAT Prep: Ratios, Proportions, & Percents

Quiz

•

9th - 10th Grade

12 questions

Exponential Growth and Decay

Quiz

•

9th Grade

12 questions

Parallel Lines Cut by a Transversal

Quiz

•

10th Grade

12 questions

Add and Subtract Polynomials

Quiz

•

9th - 12th Grade

15 questions

Combine Like Terms and Distributive Property

Quiz

•

8th - 9th Grade

20 questions

Function or Not a Function

Quiz

•

8th - 9th Grade

10 questions

Elijah McCoy: Innovations and Impact in Black History

Interactive video

•

6th - 10th Grade