Evaluate each expression 27^(-4/3)

Key Concepts

Exponents and Rational Exponents

Exponents represent repeated multiplication of a base number. Rational exponents, such as -4/3, indicate both a root and a power. The numerator indicates the power, while the denominator indicates the root. For example, a negative exponent signifies the reciprocal of the base raised to the positive exponent.

Negative Exponents

A negative exponent indicates that the base should be taken as the reciprocal. For instance, a^(-n) is equivalent to 1/(a^n). This concept is crucial for simplifying expressions with negative exponents, allowing for easier computation and understanding of the expression's value.

Cube Roots

The cube root of a number x, denoted as x^(1/3), is a value that, when multiplied by itself three times, gives x. In the expression 27^(-4/3), the denominator of the rational exponent indicates that we first take the cube root of 27, which is 3, before applying the negative exponent to find the final value.