Perform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. $$\frac{-4}{\sqrt[3]{3}$} + $\frac{1}{\sqrt[3]{24}$} - $\frac{2}{\sqrt[3]{81}$}$

검증된 단계별 안내

Identify the expression to simplify: $\left(-\frac{4}{\sqrt[3]{3}}\right) + \left(\frac{1}{\sqrt[3]{24}}\right) - \left(\frac{2}{\sqrt[3]{81}}\right)$.

Rewrite each cube root in terms of prime factors or simpler cube roots if possible: For example, $\sqrt[3]{24} = \sqrt[3]{8 \times 3} = \sqrt[3]{8} \times \sqrt[3]{3}$ and $\sqrt[3]{81} = \sqrt[3]{3^4} = \sqrt[3]{3^3 \times 3} = 3 \times \sqrt[3]{3}$.

Express each term with the simplified cube roots: Replace $\sqrt[3]{24}$ and $\sqrt[3]{81}$ with their factored forms to have a common cube root base if possible.

Find a common denominator involving $\sqrt[3]{3}$ to combine all terms into a single fraction. This may involve multiplying numerator and denominator of each term appropriately.

Combine the numerators over the common denominator and simplify the resulting expression by combining like terms.

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.

Cube Roots and Radicals

A cube root of a number is a value that, when multiplied by itself three times, gives the original number. It is denoted as ∛x. Understanding how to work with cube roots is essential for simplifying expressions involving radicals.

Simplifying Radicals

Simplifying radicals involves rewriting the radical expression in its simplest form by factoring out perfect cubes (for cube roots) or other powers. This process makes it easier to perform addition or subtraction of radical terms.

Adding and Subtracting Radical Expressions

To add or subtract radicals, the radicals must have the same radicand (the number inside the root) and index. If they differ, you must simplify or rewrite them to have a common radical form before combining the terms.

Perform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. −433+1243−2813\(\frac{-4}{\sqrt[3]{3}\)} + \(\frac{1}{\sqrt[3]{24}\)} - \(\frac{2}{\sqrt[3]{81}\)} 33−4+3241−3812

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Cube Roots and Radicals

Simplifying Radicals

Adding and Subtracting Radical Expressions

Perform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. $\(\frac{-4}{\sqrt[3]{3}\)} + \(\frac{1}{\sqrt[3]{24}\)} - \(\frac{2}{\sqrt[3]{81}\)}$