Algebra Class: Rational Exponents & Radicals

Questions and Answers

Which expression represents the same value as $x^{3/4}$?

$ oot{3}{x^4}$

$ oot{4}{x^3}$ (correct)

$rac{1}{4}x^3$

$rac{1}{3}x^{4}$

Which of the following is a correct law of radicals?

$ oot{a}{b} imes oot{a}{c} = oot{a}{bc}$ (correct)

$ oot{a}{b + c} = oot{a}{b} + oot{a}{c}$

$ oot{a}{b} imes oot{c}{d} = oot{a+c}{b imes d}$

$ oot{a}{b} = b^{a}$

What is the simplified form of $ oot{25}{x^5} imes oot{25}{x^3}$?

$ oot{25}{x^8}$ (correct)

$ oot{25}{x^{15}}$

$ oot{25}{x^4}$

$ oot{25}{x^{2}}$

Which of the following is the correct method to solve the equation $ oot{3}{x} = 4$?

<p>Cube both sides to find $x = 64$</p> Signup and view all the answers

If $y = oot{4}{x} + 3$, what is the value of $x$ when $y = 7$?

<p>$16$</p> Signup and view all the answers

Study Notes

Lesson 1: Rational Exponents

Expressions with rational exponents can be represented as ( a^{m/n} = \sqrt[n]{a^m} ), linking exponents and roots.
To simplify expressions involving rational exponents, find common bases and apply laws of exponents.
Convert rational exponent expressions into radical forms and vice versa, for instance, ( x^{1/2} = \sqrt{x} ).

Lesson 2: Radicals

The laws of radicals include ( \sqrt{a} \cdot \sqrt{b} = \sqrt{ab} ) and ( \sqrt{a/b} = \frac{\sqrt{a}}{\sqrt{b}} ).
Radical expressions can be simplified by factoring out perfect squares and reducing the radical to its simplest form.
Operations on radical expressions include addition, subtraction, multiplication, and division, requiring a common denominator when adding or subtracting.

Lesson 3: Solving Radicals

To solve equations with radical expressions, isolate the radical term and square both sides to eliminate the radical.
Verifying solutions is crucial as squaring can introduce extraneous solutions.
Problems involving radicals may require the application of rational exponents, radical simplification, and operations on radical expressions to find solutions.

Description

This quiz covers key concepts from the Algebra class focusing on rational exponents and radicals. Learn how to simplify expressions with rational exponents, apply laws of radicals, and solve equations involving radicals. Test your understanding of these fundamental topics in algebra.