Convert $$\frac{1}{2}$$ to radical form.

$$\frac{1}{2}$$ can be expressed as @@rac{1}{ oot{2}{x}}@@.

What is the value of $$x^{0}$$ for any non-zero x?

$$x^{0} = 1$$ for any non-zero value of x.

What is the product rule for exponents?

The product rule states that $$x^a \times x^b = x^{a+b}$$ .

What is the quotient rule for exponents?

The quotient rule states that $$\frac{x^a}{x^b} = x^{a-b}$$ .

How do you express $$\frac{x^{\frac{1}{2}}}{x^{\frac{1}{3}}}$$ using the quotient rule?

$$\frac{x^{\frac{1}{2}}}{x^{\frac{1}{3}}} = x^{\frac{1}{2} - \frac{1}{3}} = x^{\frac{1}{6}}$$ .

What is the power of a power rule?

The power of a power rule states that $$(x^a)^b = x^{a \times b}$$ .

Convert $$x^{-\frac{2}{3}}$$ to radical form.

@@x^{-rac{2}{3}} = rac{1}{ oot{3}{x^2}}@@.

What is the significance of a negative exponent?

A negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent. For example, $$x^{-a} = \frac{1}{x^a}$$ .

How do you evaluate $$x^{\frac{1}{2}}$$ ?

@@x^{rac{1}{2}} = oot{2}{x}@@, which is the square root of x.

What is the general form of a rational exponent?

The general form of a rational exponent is $$x^{\frac{m}{n}}$$ , where m is the power and n is the root.

LT 37 Rational Exponent Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is a rational exponent?

Back

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

What is the relationship between rational exponents and roots?

Back

4.

FLASHCARD QUESTION

Front

Back

@@x^{rac{3}{4}} = oot{4}{x^3}@@.

5.

FLASHCARD QUESTION

Front

Back

@@x^{rac{5}{2}} = oot{2}{x^5} = rac{x^5}{ oot{2}{1}}@@.

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Convert @@ oot{3}{x}@@ to exponential form.

Back

@@ oot{3}{x} = x^{rac{1}{3}}@@.

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