Match the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. -3x^1/3

Verified step by step guidance

1. Identify the rational exponent expression given: \(-3x^{\frac{1}{3}}\).
2. Recall that a rational exponent \(x^{\frac{m}{n}}\) can be rewritten as a radical expression \(\sqrt[n]{x^m}\).
3. Apply this rule to \(x^{\frac{1}{3}}\), which means the cube root of \(x\), or \(\sqrt[3]{x}\).
4. Rewrite the entire expression \(-3x^{\frac{1}{3}}\) as \(-3\sqrt[3]{x}\).
5. Match this radical expression \(-3\sqrt[3]{x}\) with the corresponding expression in Column II.

Key Concepts

Rational Exponents

Rational exponents express roots and powers simultaneously, where the numerator indicates the power and the denominator indicates the root. For example, x^(1/3) means the cube root of x, and x^(m/n) means the nth root of x raised to the mth power.

Radical Expressions

Radical expressions use root symbols to represent roots of numbers or variables. The nth root of x is written as √[n]{x}, which is equivalent to x raised to the power of 1/n. Understanding this equivalence helps in converting between radicals and rational exponents.

Properties of Exponents

Properties of exponents govern how to manipulate expressions with powers, including multiplication, division, and negative exponents. For example, a negative sign outside an expression like -3x^(1/3) indicates multiplication by -3, and understanding these rules is essential for correctly matching expressions.