OpenStax Algebra and Trigonometry - Chapter 1, Section 3

Questions and Answers

What is the expression represented by x²?

x squared (correct)

x to the first power

x to the power of 2 (correct)

x to the power of 3

What does x^(4/3) represent?

x raised to the power of 4 divided by 3 (correct)

The fourth power of x raised to the cube root

Four times x to the power of three

The cube root of x raised to the fourth power (correct)

What is x^(1/9) equal to?

x to the power of 0.1 (correct)

x multiplied by itself nine times

x to the ninth power

The ninth root of x (correct)

What does x^(1/2) represent?

The square root of x Signup and view all the answers

What does x^(1/3) symbolize?

x raised to the power of 0.33 Signup and view all the answers

What is the value of 1?

1 Signup and view all the answers

What does x represent?

variable Signup and view all the answers

What is x^(9/10)?

The tenth root of x raised to the ninth power Signup and view all the answers

What does x⁴ equal?

x multiplied by itself four times Signup and view all the answers

What does x⁷ represent?

The seventh power of x Signup and view all the answers

What is the value of 256?

256 Signup and view all the answers

What is the value of 216?

216 Signup and view all the answers

What is the value of 2?

2 Signup and view all the answers

What does 9 equal?

9 Signup and view all the answers

What is the value of 27?

27 Signup and view all the answers

What does 8 represent?

8 Signup and view all the answers

What is the value of 36?

36 Signup and view all the answers

What does 5 equal?

5 Signup and view all the answers

What is the value of 64?

64 Signup and view all the answers

What does 6 represent?

6 Signup and view all the answers

What is the value of 32?

32 Signup and view all the answers

What does 343 equal?

343 Signup and view all the answers

What does 3 represent?

3 Signup and view all the answers

What does 4 equal?

4 Signup and view all the answers

What is the value of 125?

125 Signup and view all the answers

What are square roots?

The opposite of squaring Signup and view all the answers

What are exponents?

The number that tells how many equal factors there are Signup and view all the answers

What is the leading coefficient?

The coefficient of the term with the highest degree Signup and view all the answers

What is the index of a radical?

The value of n in the radical ^n√a Signup and view all the answers

What is the simplest form of a radical?

No perfect nth powers as factors and any denominator has been rationalized Signup and view all the answers

What are like radicals?

Expressions that have the same index and same radicand Signup and view all the answers

Study Notes

Radicals and Rational Exponents

x²: Represents a variable x raised to the power of 2, indicating it is multiplied by itself.
x^(4/3): Indicates x raised to the four-thirds power, a rational exponent reflecting both multiplication and a cube root.
x^(1/9): Signifies the ninth root of x, represented as a rational exponent.
x^(1/2): Equivalent to the square root of x, illustrating a common radical form.
x^(1/3): Represents the cube root of x, a typical radical expression.
1: The multiplicative identity, representing no change when multiplied by any number.
x: The variable itself, fundamental in algebra and expressing unknown quantities.
x^(9/10): Reflects a number that is raised to the nine-tenths power, indicating both multiplication and the tenth root.
x⁴: Indicates x raised to the fourth power, showcasing a variable multiplied by itself four times.
x⁷: Depicts x raised to the seventh power, highlighting another exponential expression.
(x⁻⁷/³)⁻³: Represents the reciprocal of x raised to the seventh and divided by three, all raised to the negative third power, demonstrating the manipulation of negative exponents and fractions.
256: A perfect square, specifically (16^2) or (2^8), commonly encountered in factorization and powers.
216: Equivalent to (6^3) or (2^3 \times 3^3), signifying a perfect cube useful in radical simplification.
2: The smallest prime number, foundational in various mathematical constructs, such as factors and exponents.
9: A perfect square equal to (3^2), often used in square root calculations.
27: A perfect cube represented as (3^3), frequently involved in radical expressions.
8: A perfect cube, equivalent to (2^3), relevant in explaining cube roots.
36: A perfect square, calculated as (6^2), appearing often in equations involving roots.
5: A prime number, representing an important base in mathematics.
64: Equal to (4^3) or (2^6), recognizable as a perfect cube.
6: A composite number, noted for its factors being 1, 2, 3, and 6.
32: Expressible as (2^5), representing a notable base in powers of 2.
343: A perfect cube, calculated as (7^3), useful in cube root manipulation.
3: Another small prime number, significant in numerous mathematical operations.
4: A perfect square, expressed as (2^2), appearing frequently in calculations.
125: Recognized as (5^3), a perfect cube important in radical transformations.

Additional Concepts

Square Roots: The inverse operation to squaring a number, a fundamental concept in radical expressions.
Exponents: Denote the number of times a base is multiplied by itself, a central aspect of algebra.
Leading Coefficient: The coefficient of the term with the highest degree in a polynomial, important in polynomial expressions.
Index of a Radical: Refers to the "n" in the radical notation (n\sqrt{a}), dictating the root being taken.
Simplest Form of a Radical: A radical expressed without any perfect nth powers as factors, and with rationalized denominators.
Like Radicals: Expressions that share the same index and radicand, enabling simplification and operation consolidation.

Studying That Suits You

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Test your knowledge on radicals and rational exponents with this set of flashcards. Each card includes a mathematical expression, helping you familiarize yourself with the terminology and concepts from this section of Algebra and Trigonometry. Perfect for reinforcing your understanding and preparing for more complex problems.