Perform the indicated operations. Assume all variables represent positive real numbers. 3xxy23−28x4y233x\sqrt[3]{$$xy^2$$} - 2\sqrt[3]{$$8x^4$y^2$$} 3x3xy2−238x4y2

Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063당신이 사용하는 게 아니라요?교과서 변경

모든 교과서

Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 105

1장, 문제 105

Perform the indicated operations. Assume all variables represent positive real numbers. $3x$\sqrt$[3]{xy^2} - 2$\sqrt$[3]{8x^4y^2}$

검증된 단계별 안내

Identify the terms to be operated on: $3x\sqrt[3]{xy^{2}}$ and $2\sqrt[3]{8x^{4}y^{2}}$.

Rewrite the cube roots as fractional exponents: $\sqrt[3]{xy^{2}} = (xy^{2})^{\frac{1}{3}}$ and $\sqrt[3]{8x^{4}y^{2}} = (8x^{4}y^{2})^{\frac{1}{3}}$.

Simplify the second cube root by factoring inside the root: $8 = 2^{3}$, so $\sqrt[3]{8x^{4}y^{2}} = \sqrt[3]{2^{3} \cdot x^{4} \cdot y^{2}}$.

Apply the cube root to each factor separately: $\sqrt[3]{2^{3}} = 2$, $\sqrt[3]{x^{4}} = x^{\frac{4}{3}}$, and $\sqrt[3]{y^{2}} = y^{\frac{2}{3}}$.

Rewrite the original expression using these simplifications and then combine like terms by expressing all parts with fractional exponents to facilitate addition or subtraction.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

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

Radical Expressions and Cube Roots

Radical expressions involve roots such as square roots or cube roots. The cube root of a number x, denoted ∛x, is a value that when cubed gives x. Understanding how to simplify and manipulate cube roots is essential for combining terms involving radicals.

Properties of Exponents

Exponents indicate repeated multiplication. When working with radicals, exponents can be manipulated using rules like multiplying powers, dividing powers, and converting between radicals and fractional exponents, which helps simplify expressions under the root.

Combining Like Terms with Radicals

To perform operations like addition or subtraction on radical expressions, the terms must have the same radicand and root degree. Simplifying each radical to its simplest form allows identification of like terms, enabling proper combination of coefficients.

Perform the indicated operations. Assume all variables represent positive real numbers. 3xxy23−28x4y233x\(\sqrt\)[3]{xy^2} - 2\(\sqrt\)[3]{8x^4y^2} 3x3xy2−238x4y2

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Radical Expressions and Cube Roots

Properties of Exponents

Combining Like Terms with Radicals

Perform the indicated operations. Assume all variables represent positive real numbers. $3x\(\sqrt\)[3]{xy^2} - 2\(\sqrt\)[3]{8x^4y^2}$