Simplify each expression. Assume all variables represent nonzero real numbers. -(x³y²/z)⁰

Verified step by step guidance

1. Recall the zero exponent rule: for any nonzero expression \(a\), \(a^0 = 1\). This means that any expression raised to the zero power simplifies to 1.
2. Identify the base expression inside the parentheses: \(\left(\frac{x^{3} y^{2}}{z}\right)\).
3. Since the entire expression inside the parentheses is raised to the zero power, apply the zero exponent rule: \(\left(\frac{x^{3} y^{2}}{z}\right)^0 = 1\).
4. Now consider the negative sign outside the parentheses: \(-\left(\frac{x^{3} y^{2}}{z}\right)^0 = -1\).
5. Therefore, the simplified form of the expression is \(-1\).

Key Concepts

Zero Exponent Rule

Any nonzero base raised to the zero power equals 1. This means that for any expression like (a)^0, where a ≠ 0, the value is 1 regardless of the complexity of a.

Properties of Exponents

Exponents indicate repeated multiplication. Understanding how to manipulate powers, such as distributing exponents over products or quotients, is essential for simplifying expressions involving variables with exponents.

Sign and Negative Signs Outside Parentheses

A negative sign outside parentheses affects the entire expression inside. When simplifying, it is important to apply the negative sign correctly after evaluating the expression inside the parentheses.