Simplify each exponential expression in Exercises 23–64. x^−2y

Verified step by step guidance

1. Identify the expression: \( x^{-2}y \).
2. Recall the property of exponents: \( a^{-n} = \frac{1}{a^n} \).
3. Apply the property to \( x^{-2} \): \( x^{-2} = \frac{1}{x^2} \).
4. Rewrite the expression using the property: \( \frac{1}{x^2} \cdot y \).
5. Combine the terms: \( \frac{y}{x^2} \).

Key Concepts

Exponential Notation

Exponential notation is a mathematical shorthand that expresses repeated multiplication of a number by itself. In the expression x^−2y, the exponent indicates how many times the base (x) is multiplied. A negative exponent signifies the reciprocal of the base raised to the absolute value of the exponent, which is crucial for simplification.

Reciprocal of a Number

The reciprocal of a number is defined as 1 divided by that number. For example, the reciprocal of x is 1/x. When dealing with negative exponents, such as in x^−2, it is essential to convert the expression into its reciprocal form, which helps in simplifying the expression effectively.

Simplifying Expressions

Simplifying expressions involves reducing them to their most basic form while maintaining their equivalence. This process often includes combining like terms, applying the laws of exponents, and eliminating unnecessary components. In the case of x^−2y, simplification would require applying the rules of exponents to rewrite the expression in a more manageable format.