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Ch. R - Review of Basic Concepts
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Lial 13th EditionCh. R - Review of Basic Concepts문제 109
1장, 문제 109

Calculate each value mentally. (0.253)(4003)

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1
Recognize that the expression is a product of two cubes: \((0.25)^3\) and \((400)^3\).
Use the property of exponents that states \((a)^3 \times (b)^3 = (a \times b)^3\) to combine the terms into a single cube: \((0.25 \times 400)^3\).
Calculate the product inside the parentheses: multiply \(0.25\) by \(400\).
Rewrite the expression as the cube of the result from step 3: \((\text{result})^3\).
Finally, cube the number obtained in step 4 by multiplying it by itself three times.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Exponentiation and Powers

Exponentiation involves raising a base number to a power, which means multiplying the base by itself repeatedly. For example, 0.25³ means 0.25 × 0.25 × 0.25. Understanding how to compute powers is essential for simplifying expressions involving exponents.
추천 영상:
04:10
Powers of i

Properties of Exponents

The properties of exponents, such as (a^m)(b^m) = (ab)^m, allow us to simplify expressions by combining bases raised to the same power. This property helps in rewriting (0.25³)(400³) as (0.25 × 400)³, making mental calculation easier.
추천 영상:
04:06
Rational Exponents

Mental Math Strategies

Mental math strategies involve simplifying numbers and using known facts to calculate values quickly without paper. Recognizing that 0.25 × 400 equals 100 allows you to compute (100)³ mentally, which is simpler than calculating each power separately.
추천 영상:
4:07
Decomposition of Functions
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교과서 질문

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교과서 질문

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