Simplify each expression. 1011(22z)\frac{10}{11} (22z) 1110(22z)

Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

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Lial 13th Edition

Ch. R - Review of Basic Concepts

Problem 127

Chapter 1, Problem 127

Simplify each expression. $$\frac{10}{11}$ (22z)$

Verified step by step guidance

Identify the expression to simplify: $\frac{10}{11} (22\theta)$.

Recognize that multiplication of a fraction by a term means multiplying the numerator by the term and keeping the denominator the same: $\frac{10}{11} \times 22\theta = \frac{10 \times 22\theta}{11}$.

Multiply the constants in the numerator: $10 \times 22 = 220$, so the expression becomes $\frac{220\theta}{11}$.

Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 11: $\frac{220\theta}{11} = \frac{220 \div 11 \times \theta}{11 \div 11} = 20\theta$.

Write the simplified expression as $20\theta$.

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Key Concepts

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

Simplifying Algebraic Expressions

Simplifying algebraic expressions involves combining like terms and reducing fractions to their simplest form. This process makes expressions easier to work with and understand by eliminating unnecessary complexity.

Multiplying Fractions and Variables

When multiplying fractions, multiply the numerators together and the denominators together. Variables multiply by following the laws of exponents, such as combining powers when the same base is involved.

Distributive Property

The distributive property allows you to multiply a single term by each term inside a parenthesis. It is useful for expanding expressions and simplifying products involving sums or differences.

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Textbook Question

Multiply or divide as indicated. 124.03 ÷ 100

Textbook Question

Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers. See Example 8.

$7 (5 t + 3)^{- \frac{5}{3}} + 14 (5 t + 3)^{- \frac{2}{3}} - 21 (5 t + 3)^{\frac{1}{3}}$

Textbook Question

Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers. See Example 8. 2(3x+1)^-3/2+4(3x+1)^-1/2+6(3x+1)^1/2

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Textbook Question

Multiply or divide as indicated. 23.29÷1000

Textbook Question

Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers. See Example 8.

$(3 r + 1)^{- \frac{2}{3}} + (3 r + 1)^{\frac{1}{3}} + (3 r + 1)^{\frac{4}{3}}$