Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. (y^7/3)(y^-4/3)

Key Concepts

Exponents and Their Properties

Exponents represent repeated multiplication of a base number. Key properties include the product of powers (a^m * a^n = a^(m+n)) and the power of a power (a^m)^n = a^(m*n). Understanding these properties is essential for simplifying expressions involving exponents, especially when combining terms with the same base.

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the opposite positive exponent (a^-n = 1/a^n). This concept is crucial when simplifying expressions, as it allows for the conversion of negative exponents into a more manageable form, ensuring that the final answer adheres to the requirement of not having negative exponents.

Simplifying Algebraic Expressions

Simplifying algebraic expressions involves combining like terms and applying exponent rules to reduce the expression to its simplest form. This process often includes eliminating negative exponents and ensuring that all variables are expressed positively, which is a common requirement in algebraic problems.