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

Exponents

College Algebra

0. Review of Algebra

Exponents

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1:55 minutes

Problem 27

Textbook Question

Evaluate each exponential expression: (3^3)/(3^6)

Verified step by step guidance

Identify the base and the exponents in the expression: \( \frac{3^3}{3^6} \).

Apply the quotient rule for exponents, which states \( \frac{a^m}{a^n} = a^{m-n} \), where \( a \) is the base and \( m \) and \( n \) are the exponents.

Subtract the exponent in the denominator from the exponent in the numerator: \( 3^{3-6} \).

Simplify the expression by calculating the new exponent: \( 3^{-3} \).

Recognize that a negative exponent indicates a reciprocal, so \( 3^{-3} = \frac{1}{3^3} \).

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Key Concepts

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

Exponential Expressions

Exponential expressions involve a base raised to a power, indicating how many times the base is multiplied by itself. For example, in the expression 3^3, the base is 3 and the exponent is 3, meaning 3 is multiplied by itself three times (3 × 3 × 3). Understanding how to manipulate these expressions is crucial for evaluating them correctly.

Laws of Exponents

The laws of exponents provide rules for simplifying expressions involving powers. One key rule is that when dividing two exponential expressions with the same base, you subtract the exponents: a^m / a^n = a^(m-n). This principle is essential for evaluating expressions like (3^3)/(3^6), as it allows for straightforward simplification.

Simplification of Fractions

Simplifying fractions involves reducing them to their simplest form, which can include canceling common factors. In the context of exponential expressions, this means applying the laws of exponents to rewrite the expression in a more manageable form. For instance, after applying the laws of exponents to (3^3)/(3^6), the result can be expressed as 1/3^3, illustrating the importance of simplification in mathematical evaluations.