Find each root. ∛x³

Verified step by step guidance

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.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

45s

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

Recommended video:

Guided course