How do you simplify $$x^{\frac{3}{4}} \times x^{\frac{1}{2}}$$ ?

Using the product of powers property: $$x^{\frac{3}{4}} \times x^{\frac{1}{2}} = x^{\frac{3}{4} + \frac{2}{4}} = x^{\frac{5}{4}}$$ .

How do you simplify $$\frac{y^{\frac{5}{3}}}{y^{\frac{2}{3}}}$$ ?

Using the quotient of powers property: $$\frac{y^{\frac{5}{3}}}{y^{\frac{2}{3}}} = y^{\frac{5}{3} - \frac{2}{3}} = y^{\frac{3}{3}} = y^1 = y$$ .

What is the zero exponent rule?

The zero exponent rule states that any non-zero base raised to the power of zero equals one: $$a^0 = 1$$ , where @@a eq 0@@.

How do you express $$\frac{1}{x^{\frac{3}{2}}}$$ using negative exponents?

Using the negative exponent rule: $$\frac{1}{x^{\frac{3}{2}}} = x^{-\frac{3}{2}}$$ .

What is the simplified form of $$3x^{\frac{-1}{4}}y^{\frac{5}{3}} \times -2x^{\frac{4}{3}}y^{-\frac{7}{5}}$$ ?

The simplified form is $$-6x^{\frac{13}{12}}y^{\frac{4}{15}}$$ .

How do you simplify $$\frac{24x^{\frac{3}{4}}y^3}{40x^{\frac{5}{2}}y^{-\frac{2}{3}}}$$ ?

The simplified form is $$\frac{3y^{\frac{11}{3}}}{5x^{\frac{7}{4}}}$$ .

What is the relationship between rational exponents and roots?

Rational exponents represent roots; for example, $$x^{\frac{1}{n}}$$ represents the nth root of x.

How do you write @@ oot[4]{x^5}@@ in exponential form?

In exponential form, it is written as $$x^{\frac{5}{4}}$$ .

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

Using the product of powers property: $$x^{\frac{1}{2} + \frac{1}{3}} = x^{\frac{3}{6} + \frac{2}{6}} = x^{\frac{5}{6}}$$ .

What does it mean to simplify an expression with rational exponents?

Simplifying an expression with rational exponents means to reduce it to its simplest form, combining like terms and applying exponent rules.

Properties of Rational Exponents Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a rational exponent?

Back

Tags

CCSS.HSN.RN.A.2

2.

FLASHCARD QUESTION

Front

How do you convert a radical expression to exponential form?

Back

3.

FLASHCARD QUESTION

Front

What is the product of powers property?

Back

Tags

CCSS.8.EE.A.1

4.

FLASHCARD QUESTION

Front

What is the quotient of powers property?

Back

Tags

CCSS.8.EE.A.1

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.8.EE.A.1

6.

FLASHCARD QUESTION

Front

What is the power of a power property?

Back

Tags

CCSS.8.EE.A.1

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.8.EE.A.1

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