How do you simplify $$ \frac{a^{-3}}{a^{-1}} $$ ?

You can simplify it by subtracting the exponents: $$ a^{-3 - (-1)} = a^{-2} = \frac{1}{a^2} $$ .

How do you simplify $$ \text{√}5 \times \text{√}10 $$ ?

You can multiply the radicands: $$ \text{√}(5 \times 10) = \text{√}50 = 5\text{√}2 $$ .

What is the value of $$ (2ab)^3 $$ ?

You can apply the power of a product rule: $$ (2^3)(a^3)(b^3) = 8a^3b^3 $$ .

What is the exponential form of $$ \text{∜}(3x)^3 $$ ?

The exponential form is $$ (3x)^{3/4} $$ .

What is the result of $$ (-4r^5)(2r^8) $$ ?

You multiply the coefficients and add the exponents: $$ -8r^{5+8} = -8r^{13} $$ .

What is the definition of a rational exponent?

A rational exponent is an exponent that is a fraction, indicating both a power and a root. For example, $$ x^{m/n} = \text{∜}(x^m) $$ .

What is the zero exponent rule?

Any non-zero base raised to the power of zero equals one: $$ a^0 = 1 $$ .

How do you express $$ \text{√}x^2 $$ in terms of exponents?

You can express it as $$ x^{2/2} = x^1 = x $$ .

What is the simplified form of $$ (x^3)^2 $$ ?

You multiply the exponents: $$ x^{3 \times 2} = x^6 $$ .

Working with Exponents and Radicals Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the product of two powers with the same base?

Back

2.

FLASHCARD QUESTION

Front

What is the power of a product rule?

Back

3.

FLASHCARD QUESTION

Front

What is the power of a quotient rule?

Back

4.

FLASHCARD QUESTION

Front

What is the definition of a negative exponent?

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is the definition of a radical?

Back

7.

FLASHCARD QUESTION

Front

What is the relationship between exponents and roots?

Back

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

10 questions

Novice Lesson 2 Practice Words

Flashcard

•

KG

7 questions

International Yoga Day Quiz

Flashcard

•

KG - University

15 questions

Clothing and Accessories Vocabulary

Flashcard

•

KG - University

4 questions

5.2. Asymptotes Verticales

Flashcard

•

9th - 12th Grade

13 questions

I. világháború eseményei

Flashcard

•

11th Grade

9 questions

Classical and Medieval Art

Flashcard

•

KG

Popular Resources on Wayground

8 questions

Spartan Way - Classroom Responsible

Quiz

•

9th - 12th Grade

15 questions

Fractions on a Number Line

Quiz

•

3rd Grade

14 questions

Boundaries & Healthy Relationships

Lesson

•

6th - 8th Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

3 questions

Integrity and Your Health

Lesson

•

6th - 8th Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

9 questions

FOREST Perception

Lesson

•

KG

20 questions

Main Idea and Details

Quiz

•

5th Grade

Discover more resources for Mathematics

20 questions

Graphing Inequalities on a Number Line

Quiz

•

6th - 9th Grade

11 questions

Adding and Subtracting Polynomials

Quiz

•

9th Grade

20 questions

Box and Whisker Plots

Quiz

•

9th Grade

18 questions

Exponential Growth and Decay

Quiz

•

9th Grade

25 questions

Logos

Quiz

•

12th Grade

12 questions

Equation of a Circle

Lesson

•

10th Grade

12 questions

Exponential Growth and Decay

Quiz

•

9th Grade

14 questions

Making Inferences From Samples

Quiz

•

7th - 12th Grade