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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 110
Chapter 1, Problem 110

Calculate each value mentally. (242)(0.52)

Verified step by step guidance
1
Recognize that the expression is a product of two squares: \((24^2)(0.5^2)\).
Recall the property of exponents that states \((a^m)(b^m) = (ab)^m\). Apply this to rewrite the expression as \((24 \times 0.5)^2\).
Calculate the product inside the parentheses: \(24 \times 0.5\).
Square the result obtained from the previous step to find \((24 \times 0.5)^2\).
This final value is the result of the original expression \((24^2)(0.5^2)\).

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Key Concepts

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

Exponentiation

Exponentiation is the process of raising a base number to a power, indicating how many times the base is multiplied by itself. For example, 24² means 24 multiplied by 24. Understanding this helps in simplifying expressions involving powers.
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Multiplication of Powers

When multiplying numbers raised to powers, each term is evaluated separately before multiplying the results. For instance, (24²)(0.5²) means calculate 24² and 0.5² individually, then multiply the two results together.
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Mental Math Strategies

Mental math involves simplifying calculations without paper or a calculator by using number properties and estimation. Recognizing squares of common numbers and decimals, like 0.5² = 0.25, aids in quickly solving problems mentally.
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