Find each root. ∛x³

Verified step by step guidance

1. Recognize that the expression \( \sqrt[3]{x^3} \) involves taking the cube root of \( x^3 \).
2. Recall the property of exponents and roots: \( \sqrt[n]{a^n} = a \) for any real number \( a \) and positive integer \( n \).
3. Apply this property to the expression: \( \sqrt[3]{x^3} = x \).
4. Understand that the cube root and the cube power are inverse operations, which means they cancel each other out.
5. Conclude that the root of \( x^3 \) when taking the cube root is simply \( x \).

Key Concepts

Cube Root

The cube root of a number is a value that, when multiplied by itself three times, gives the original number. It is denoted as ∛x, where x is the number. For example, the cube root of 27 is 3, since 3 × 3 × 3 = 27. Understanding cube roots is essential for solving equations involving cubic expressions.

Exponents and Radicals

Exponents represent repeated multiplication, while radicals are the inverse operation. The expression x³ indicates that x is multiplied by itself three times. The cube root operation, ∛, is a radical that undoes the exponentiation of 3. Mastery of these concepts is crucial for manipulating and solving algebraic expressions.

Solving Equations

Solving equations involves finding the values of variables that satisfy the equation. In the case of ∛x³, we are looking for the value of x that, when cubed, equals the original expression. This process often requires understanding the properties of equality and inverse operations, which are foundational in algebra.