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Ch. R - Review of Basic Concepts
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. R - Review of Basic ConceptsProblem 5
Chapter 1, Problem 5

Perform the indicated operation, and write each answer in lowest terms. 2x/5 ∙ 10/x2

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Identify the given expression to multiply: \(\frac{2x}{5} \times \frac{10}{x^{2}}\).
Multiply the numerators together and the denominators together: \(\frac{2x \times 10}{5 \times x^{2}}\).
Simplify the numerator and denominator separately: numerator becomes \$20x\(, denominator becomes \)5x^{2}$, so the expression is \(\frac{20x}{5x^{2}}\).
Factor and reduce common factors in numerator and denominator: divide both numerator and denominator by \$5x$ to simplify the fraction.
Write the simplified expression after canceling common factors, ensuring the answer is in lowest terms.

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Key Concepts

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

Multiplication of Rational Expressions

Multiplying rational expressions involves multiplying the numerators together and the denominators together. Each expression is treated like a fraction, so the product is a new fraction formed by these products.
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Simplifying Algebraic Expressions

Simplifying involves reducing expressions to their simplest form by canceling common factors in the numerator and denominator. This often requires factoring and recognizing common terms to eliminate.
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Exponents and Their Properties

Understanding how to handle exponents is crucial, especially when multiplying terms with the same base. The product rule states that when multiplying like bases, you add their exponents, which helps simplify expressions involving powers.
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Fill in the blank(s) to correctly complete each sentence. In the expression 63, 6 is the ____ , and 3 is the ____ .

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Work each problem. Match each polynomial in Column I with its factored form in Column II.

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Identify the set { 1,1/3, 1/9 ,1/27, ....} as finite or infinite.

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Which choice shows the correct way to write 1624\(\frac{16}{24}\) in lowest terms?

A. 1624=8+88+16=816=12A.\(\text{ }\]\frac{16}{24}\)=\(\frac{8+8}{8+16}\)=\(\frac{8}{16}\)=\(\frac\)12

B. 1624=4⋅44⋅6=46B.\(\text{ }\]\frac{16}{24}\)=\(\frac{4\cdot4}{4\cdot6}\)=\(\frac\)46

C. 1624=8⋅28⋅3=23C.\(\text{ }\]\frac{16}{24}\)=\(\frac{8\cdot2}{8\cdot3}\)=\(\frac{2}{3}\)

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