How do you simplify $$\frac{a^m}{a^n}$$ ?

You can simplify it using the property of exponents: $$\frac{a^m}{a^n} = a^{m-n}$$ .

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

The simplified form is $$\frac{1}{x^{\frac{2}{3}}}$$ .

What is the simplified form of $$6\text{√}2 \times 5\text{√}14$$ ?

The simplified form is $$60\text{√}7$$ .

What is the value of $$\text{√}x^2$$ ?

The value is $$|x|$$ , which is the absolute value of x.

How do you evaluate $$x^{\frac{1}{n}}$$ for positive x?

To evaluate $$x^{\frac{1}{n}}$$ , find the n-th root of x.

What is the simplified form of $$\frac{1}{\text{√}x}$$ ?

The simplified form is $$\frac{\text{√}x}{x}$$ .

What is the product property of exponents?

The product property states that $$a^m \times a^n = a^{m+n}$$ .

How do you simplify $$\frac{a^{\frac{1}{2}}}{a^{\frac{1}{3}}}$$ ?

You can simplify it to $$a^{\frac{1}{2} - \frac{1}{3}} = a^{\frac{1}{6}}$$ .

What is the quotient property of exponents?

The quotient property states that $$\frac{a^m}{a^n} = a^{m-n}$$ .

What is the value of $$\text{√}(-1)$$ ?

The value is an imaginary number, represented as $$i$$ .

Radicals & Rational Exponents Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a radical?

Back

A radical is an expression that includes a root, such as a square root (√) or cube root (∛). For example, √4 = 2.

2.

FLASHCARD QUESTION

Front

What is a rational exponent?

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

What is the relationship between radicals and rational exponents?

Back

5.

FLASHCARD QUESTION

Front

How do you convert a radical to a rational exponent?

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

How do you multiply radicals?

Back

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