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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1:14 minutes

Problem 46

Textbook Question

Multiply or divide as indicated. Write answers in lowest terms as needed. 8/(4/9)

Verified step by step guidance

Identify the operation: We need to divide 8 by \( \frac{4}{9} \).

Recall that dividing by a fraction is the same as multiplying by its reciprocal.

Find the reciprocal of \( \frac{4}{9} \), which is \( \frac{9}{4} \).

Rewrite the expression as a multiplication: \( 8 \times \frac{9}{4} \).

Multiply the whole number by the fraction: \( 8 \times \frac{9}{4} = \frac{8 \times 9}{4} \). Simplify the fraction if possible.

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Key Concepts

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

Division of Fractions

Dividing by a fraction is equivalent to multiplying by its reciprocal. For example, dividing by 4/9 means multiplying by 9/4. This concept is essential for simplifying expressions involving fractions and is a fundamental operation in algebra.

Simplifying Fractions

Simplifying fractions involves reducing them to their lowest terms, which means expressing them in a form where the numerator and denominator have no common factors other than 1. This process is crucial for presenting answers clearly and concisely in algebra.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order, which is vital when solving complex expressions.