How do you simplify $$\frac{a^{\frac{7}{2}}}{a^3}$$ ?

Using the law of exponents for division, you subtract the exponents: $$a^{\frac{7}{2} - 3} = a^{\frac{7}{2} - \frac{6}{2}} = a^{\frac{1}{2}}$$ .

What is the result of $$\text{sqrt}(x^2)$$ ?

The result is $$x$$ , assuming x is non-negative.

How do you multiply $$\text{sqrt}(a) \times \text{sqrt}(b)$$ ?

You can combine the radicals: $$\text{sqrt}(a) \times \text{sqrt}(b) = \text{sqrt}(ab)$$ .

What is the simplified form of $$\text{sqrt}(x^4)$$ ?

The simplified form is $$x^2$$ , assuming x is non-negative.

What is the product of $$\text{sqrt}(2) \times \text{sqrt}(8)$$ ?

The product is $$\text{sqrt}(16) = 4$$ .

What does it mean to rationalize the denominator?

Rationalizing the denominator means to eliminate any radicals in the denominator of a fraction. For example, to rationalize $$\frac{1}{\text{sqrt}(2)}$$ , multiply the numerator and denominator by $$\text{sqrt}(2)$$ to get $$\frac{\text{sqrt}(2)}{2}$$ .

What is the result of $$\frac{\text{sqrt}(a^2)}{a}$$ ?

The result is $$1$$ , assuming a is non-negative.

How do you divide $$\text{sqrt}(x^6)$$ by $$\text{sqrt}(x^2)$$ ?

You can simplify it as follows: $$\frac{\text{sqrt}(x^6)}{\text{sqrt}(x^2)} = \text{sqrt}\frac{x^6}{x^2} = \text{sqrt}(x^4) = x^2$$ .

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

Using the law of exponents for division, the simplified form is $$a^{\frac{4}{3} - \frac{1}{3}} = a^{\frac{3}{3}} = a$$ .

What is the result of multiplying $$\text{sqrt}(3) \times \text{sqrt}(12)$$ ?

The result is $$\text{sqrt}(36) = 6$$ .

Multiply & Divide Radical Expressions w/ Laws of Exponents Flashcards

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14 questions

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1.

FLASHCARD QUESTION

Front

What is a radical expression?

Back

Tags

CCSS.8.NS.A.1

2.

FLASHCARD QUESTION

Front

What does it mean to multiply radical expressions?

Back

3.

FLASHCARD QUESTION

Front

What is the law of exponents for multiplying powers with the same base?

Back

Tags

CCSS.8.EE.A.1

4.

FLASHCARD QUESTION

Front

What is the law of exponents for dividing powers with the same base?

Back

Tags

CCSS.8.EE.A.1

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.8.EE.A.1

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

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