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

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Identify the expression to simplify: \(x^{-2}y\). Notice that \(x\) has a negative exponent.

Recall the rule for negative exponents: \(a^{-n} = \frac{1}{a^n}\), where \(a \neq 0\) and \(n\) is a positive integer.

Apply the negative exponent rule to \(x^{-2}\), rewriting it as \(\frac{1}{x^2}\).

Rewrite the entire expression by substituting \(x^{-2}\) with \(\frac{1}{x^2}\), so the expression becomes \(\frac{y}{x^2}\).

Check if the expression can be simplified further. Since \(y\) and \(x^2\) have no common factors, the simplified form is \(\frac{y}{x^2}\).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Negative Exponents

A negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent. For example, x^(-2) equals 1 divided by x squared, or 1/x^2. Understanding this helps simplify expressions with negative powers.

Product of Powers

When multiplying expressions with the same base, add their exponents. For instance, x^a * x^b = x^(a+b). This rule is essential when simplifying expressions involving multiple powers of the same variable.

Variables and Exponents

Each variable in an expression is treated independently with its exponent. For example, in x^(-2)y, x and y are separate factors, so the exponent applies only to x. Recognizing this prevents incorrect combining of terms.

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