Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. (x^1/4y^2/5)^20/x^2

Exponents represent repeated multiplication of a base number. The power indicates how many times the base is multiplied by itself. For example, x^3 means x multiplied by itself three times. Understanding the laws of exponents, such as the product of powers and power of a power, is crucial for simplifying expressions involving exponents.

Negative exponents indicate the reciprocal of the base raised to the opposite positive exponent. For instance, x^-n equals 1/x^n. In simplification, it is essential to rewrite any negative exponents as positive to adhere to the problem's requirement of expressing answers without negative exponents, which often involves moving terms between the numerator and denominator.

Simplifying algebraic expressions involves combining like terms, applying the laws of exponents, and reducing fractions. This process often requires factoring, distributing, and canceling common factors. The goal is to express the expression in its simplest form, which is particularly important in problems that involve multiple variables and exponents.