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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 93
1장, 문제 93

Simplify using properties of exponents. 20x125x14\(\frac{20x^{\frac{1}{2}\)}}{5x^{\(\frac{1}{4}\)}}

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1
Identify the expression to simplify: \(\frac{20x^{\frac{1}{2}}}{5x^{\frac{1}{4}}}\).
Simplify the coefficients (numerical parts) by dividing 20 by 5: \(\frac{20}{5} = 4\).
Apply the quotient rule for exponents to the variable part: \(\frac{x^{\frac{1}{2}}}{x^{\frac{1}{4}}} = x^{\frac{1}{2} - \frac{1}{4}}\).
Subtract the exponents: \(\frac{1}{2} - \frac{1}{4} = \frac{2}{4} - \frac{1}{4} = \frac{1}{4}\), so the variable part becomes \(x^{\frac{1}{4}}\).
Combine the simplified coefficient and variable parts to write the simplified expression: \(4x^{\frac{1}{4}}\).

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주요 개념

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

Properties of Exponents

Properties of exponents are rules that simplify expressions involving powers of the same base. Key properties include the quotient rule, which states that when dividing like bases, subtract the exponents (a^m / a^n = a^(m-n)). These rules help in simplifying expressions with fractional exponents.
추천 영상:
04:06
Rational Exponents

Fractional Exponents

Fractional exponents represent roots and powers simultaneously. For example, x^(1/2) means the square root of x, and x^(1/4) means the fourth root of x. Understanding how to manipulate fractional exponents is essential for simplifying expressions involving roots.
추천 영상:
04:06
Rational Exponents

Simplifying Rational Expressions

Simplifying rational expressions involves reducing fractions by factoring and canceling common terms. When variables with exponents appear in numerator and denominator, apply exponent rules to combine or reduce terms, making the expression simpler and easier to interpret.
추천 영상:
05:07
Simplifying Algebraic Expressions
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