Rational Exponents

A rational exponent is an exponent that can be expressed as a fraction, where the numerator is a power and the denominator indicates the root. For example, x^(1/n) is a rational exponent.

To convert a rational exponent to a radical expression, use the formula: x^(m/n) = n√(x^m), where m is the numerator and n is the denominator.

x^(1/8) = 8√(x).

x^(11/2) = √(x^11).

To convert a radical expression to a rational exponent, use the formula: n√(x^m) = x^(m/n), where m is the power and n is the root.

√[3]{x^6} = x^(6/3) = x^2.

√[3]{x^7} = x^(7/3).

√[5]{x^3} = x^(3/5).

Rational exponents represent both powers and roots, where the denominator of the exponent indicates the root and the numerator indicates the power.

x^(m/n) = n√(x^m).