Simplify by reducing the index of the radical : [y^3]^(1/6)

Verified step by step guidance

1. Identify the expression: \( (y^3)^{1/6} \).
2. Apply the power of a power property: \((a^m)^n = a^{m \cdot n}\).
3. Multiply the exponents: \(3 \cdot \frac{1}{6}\).
4. Simplify the multiplication: \(y^{3/6}\).
5. Reduce the fraction: \(y^{1/2}\).

Key Concepts

Radical Expressions

Radical expressions involve roots, such as square roots or cube roots, represented by the radical symbol (√). The index of a radical indicates the degree of the root; for example, a square root has an index of 2, while a cube root has an index of 3. Understanding how to manipulate these expressions is crucial for simplification.

Exponents and Fractional Powers

Exponents represent repeated multiplication, and fractional exponents indicate roots. For instance, an exponent of 1/6 means taking the sixth root of a number. This concept is essential for simplifying radical expressions, as it allows us to rewrite radicals in exponential form, making calculations easier.

Simplifying Radicals

Simplifying radicals involves reducing the expression to its simplest form by factoring out perfect squares or cubes. This process often includes rewriting the radical in terms of its prime factors and applying the properties of exponents to reduce the index. Mastery of this concept is key to effectively simplifying expressions like [y^3]^(1/6).