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Ch. P - Fundamental Concepts of Algebra
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Blitzer 8th EditionCh. P - Fundamental Concepts of Algebra문제 113
1장, 문제 113

In Exercises 111–114, simplify each expression. Assume that all variables represent positive numbers. (x−5/4y1/3x−3/4)−6

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Step 1: Start by simplifying the expression inside the parentheses. Combine the exponents of x using the property of exponents: a^m * a^n = a^(m+n). Here, x^(-5/4) * x^(-3/4) becomes x^(-5/4 - 3/4).
Step 2: Simplify the exponent of x. Add the fractions in the exponent: -5/4 - 3/4 = -8/4 = -2. So, the expression inside the parentheses becomes x^(-2) * y^(1/3).
Step 3: Apply the outer exponent of -6 to each term inside the parentheses using the property (a * b)^m = a^m * b^m. This gives (x^(-2))^(-6) * (y^(1/3))^(-6).
Step 4: Simplify each term by multiplying the exponents. For x^(-2)^(-6), multiply -2 and -6 to get x^(12). For y^(1/3)^(-6), multiply 1/3 and -6 to get y^(-2).
Step 5: Combine the simplified terms. The final expression is x^(12) * y^(-2). If needed, rewrite y^(-2) as 1/y^2 to express the result without negative exponents.

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주요 개념

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

Exponents and Negative Exponents

Exponents represent repeated multiplication of a base number. A negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent. For example, x^(-a) = 1/(x^a). Understanding how to manipulate negative exponents is crucial for simplifying expressions involving them.
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Rational Exponents

Fractional Exponents

Fractional exponents indicate both a power and a root. For instance, x^(m/n) means the n-th root of x raised to the m-th power. This concept is essential for simplifying expressions that involve roots and powers simultaneously, allowing for a clearer understanding of the relationships between different terms.
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04:06
Rational Exponents

Simplifying Algebraic Expressions

Simplifying algebraic expressions involves combining like terms, applying exponent rules, and reducing fractions. This process often requires careful attention to the order of operations and the properties of exponents. Mastery of simplification techniques is vital for solving complex algebraic problems efficiently.
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05:07
Simplifying Algebraic Expressions
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