Rational Exponents

A rational exponent is an exponent that is expressed as a fraction, where the numerator indicates the power and the denominator indicates the root.

To convert a rational exponent a^(m/n) to radical form, it can be expressed as the n-th root of a raised to the m power: a^(m/n) = n√(a^m).

2^(1/6) represents the sixth root of 2.

A negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent: a^(-n) = 1/(a^n).

(5x)^(-5/4) can be simplified to 1/((5x)^(5/4)).

m^(-0.5) is equivalent to 1/(√m) or 1/(m^(1/2)).

6^(3/2) can be evaluated as √(6^3) or (√6)^3.

7^(4/3) represents the cube root of 7 raised to the fourth power: 7^(4/3) = ³√(7^4).

Rational exponents provide a way to express roots in exponential form, where the denominator of the exponent indicates the root.

To multiply two expressions with rational exponents, you can add the exponents if the bases are the same: a^(m/n) * a^(p/q) = a^((mq + np)/(nq)).