What is the relationship between exponents and roots?

Roots can be expressed as fractional exponents; for example, $$\sqrt[n]{x} = x^{\frac{1}{n}}$$ .

8.1 nth Roots Review Flashcards: 15 Cards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the exponential form of $\frac{1}{\left(\sqrt[3]{x^2}\right)}$ ?

Back

$x^{-\frac{2}{3}}$

2.

FLASHCARD QUESTION

Front

Convert $\left(5n\right)^{\frac{3}{2}}$ to radical form.

Back

$\sqrt[]{\left(5n\right)^3}$

3.

FLASHCARD QUESTION

Front

Solve the equation $\left(x+2\right)^5=-1024$ .

Back

-6

4.

FLASHCARD QUESTION

Front

What is the definition of an nth root?

Back

An nth root of a number x is a number r such that $r^n = x$ .

5.

FLASHCARD QUESTION

Front

What is the radical form of $x^{\frac{1}{2}}$ ?

Back

$\sqrt{x}$

6.

FLASHCARD QUESTION

Front

What is the value of $\sqrt[3]{27}$ ?

Back

3

7.

FLASHCARD QUESTION

Front

Express $x^{-3}$ in radical form.

Back

$\frac{1}{\sqrt[3]{x^3}}$

8.

FLASHCARD QUESTION

Front

What is the definition of a square root?

Back

A square root of a number x is a number r such that $r^2 = x$ .

9.

FLASHCARD QUESTION

Front

Convert $\sqrt[4]{16}$ to exponential form.

Back

$16^{\frac{1}{4}}$ .

10.

FLASHCARD QUESTION

Front

What is the value of $\sqrt{49}$ ?

Back

7

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