Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Radical Expressions

College Algebra

0. Review of Algebra

Radical Expressions

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2:33 minutes

Problem 99

Textbook Question

In Exercises 85–116, simplify each exponential expression.6x²/2x⁻⁸

Verified step by step guidance

Identify the expression: \( \frac{6x^2}{2x^{-8}} \).

Simplify the coefficients: \( \frac{6}{2} = 3 \).

Apply the quotient rule for exponents: \( x^a / x^b = x^{a-b} \).

Subtract the exponents: \( x^{2 - (-8)} = x^{2 + 8} = x^{10} \).

Combine the simplified coefficient and the simplified variable expression: \( 3x^{10} \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Exponential Rules

Exponential rules are fundamental properties that govern the manipulation of expressions involving exponents. Key rules include the product of powers (a^m * a^n = a^(m+n)), the quotient of powers (a^m / a^n = a^(m-n)), and the power of a power ( (a^m)^n = a^(m*n)). Understanding these rules is essential for simplifying expressions with exponents effectively.

Simplifying Rational Expressions

Simplifying rational expressions involves reducing fractions to their simplest form by canceling common factors in the numerator and denominator. This process often requires factoring polynomials and recognizing equivalent expressions. Mastery of this concept is crucial for solving problems that involve division of algebraic terms.

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the opposite positive exponent (a^(-n) = 1/a^n). This concept is vital when simplifying expressions that contain negative exponents, as it allows for the transformation of the expression into a more manageable form. Recognizing and applying this rule is key to achieving the correct simplification.