Find each root. ∛x³

검증된 단계별 안내

Recognize that the expression is the cube root of \(x^3\), which can be written as \(\sqrt[3]{x^3}\).

Recall the property of radicals and exponents: \(\sqrt[n]{a^m} = a^{\frac{m}{n}}\). Applying this, rewrite the expression as \(x^{\frac{3}{3}}\).

Simplify the exponent \(\frac{3}{3}\) to 1, so the expression becomes \(x^1\).

Understand that \(x^1\) is simply \(x\), so the cube root of \(x^3\) simplifies to \(x\).

Note that this simplification holds for all real numbers \(x\), considering the cube root function is defined for all real numbers.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

45s

도움이 되었나요?

주요 개념

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

Cube Roots

The cube root of a number is a value that, when multiplied by itself three times, gives the original number. For example, the cube root of 8 is 2 because 2³ = 8. Cube roots can be positive, negative, or zero.

Properties of Exponents

Exponents indicate how many times a base is multiplied by itself. Key properties include that (a^m)^n = a^(m*n) and that roots can be expressed as fractional exponents, such as the cube root of x being x^(1/3).

Simplifying Radical Expressions

Simplifying radicals involves rewriting expressions to their simplest form. For cube roots, this means recognizing when the radicand is a perfect cube, allowing the root and exponent to cancel out, such as ∛(x³) = x.