In Exercises 91–100, simplify using properties of exponents. (x^2/3)^3

Key Concepts

Properties of Exponents

The properties of exponents are rules that govern how to manipulate expressions involving powers. Key properties include the product of powers (a^m * a^n = a^(m+n)), the power of a power ((a^m)^n = a^(m*n)), and the quotient of powers (a^m / a^n = a^(m-n)). Understanding these properties is essential for simplifying expressions with exponents.

Power of a Power Rule

The power of a power rule states that when raising a power to another power, you multiply the exponents. For example, (a^m)^n simplifies to a^(m*n). This rule is crucial for simplifying expressions like (x^(2/3))^3, as it allows you to combine the exponents effectively.

Fractional Exponents

Fractional exponents represent roots in addition to powers. For instance, an exponent of 1/2 corresponds to the square root, while 2/3 indicates the cube root of the square. Understanding how to interpret and manipulate fractional exponents is vital for simplifying expressions that involve them, such as (x^(2/3))^3.