Simplify by reducing the index of the radical : y36\sqrt[6]{$$y^3$$}

Ch. P - Fundamental Concepts of Algebra

Blitzer8th EditionCollege AlgebraISBN: 9780136970514당신이 사용하는 게 아니라요?교과서 변경

모든 교과서

Blitzer 8th Edition

Ch. P - Fundamental Concepts of Algebra

문제 72

1장, 문제 72

Simplify by reducing the index of the radical : $\sqrt[6]{y^{3}}$

검증된 단계별 안내

Recognize that the expression $ [y^3]^{1/6} $ is a radical expression written with rational exponents. The exponent $ \frac{1}{6} $ represents the sixth root.

Use the property of exponents that $ (a^m)^n = a^{m \times n} $ to combine the powers inside the expression.

Multiply the exponents: $ 3 \times \frac{1}{6} = \frac{3}{6} $. So, the expression becomes $ y^{\frac{3}{6}} $.

Simplify the fraction $ \frac{3}{6} $ to its lowest terms, which is $ \frac{1}{2} $. Now the expression is $ y^{\frac{1}{2}} $.

Recognize that $ y^{\frac{1}{2}} $ is equivalent to the square root of $ y $, or $ \sqrt{y} $. This is the simplified form with the reduced index.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

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

Radical and Rational Exponents

Radicals and rational exponents represent the same mathematical operation. For example, the nth root of a number can be written as that number raised to the power of 1/n. Understanding this equivalence allows simplification of expressions involving roots and fractional powers.

Properties of Exponents

The properties of exponents, such as (a^m)^n = a^(m*n), are essential for simplifying expressions with powers raised to other powers. Applying these rules helps combine and reduce exponents efficiently, which is crucial in simplifying radical expressions.

Reducing the Index of a Radical

Reducing the index of a radical involves rewriting the expression to have a smaller root index or converting it into a simpler form using exponent rules. This process often makes the expression easier to interpret or further simplify.

Simplify by reducing the index of the radical : y36\(\sqrt\)[6]{y^3}