Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3.-(p²q³/r³)⁰

Verified step by step guidance

1. Recall the zero exponent rule: for any nonzero expression \(a\), \(a^0 = 1\).
2. Identify the base expression inside the parentheses: \(\left(\frac{p^2 q^3}{r^3}\right)\).
3. Since the entire expression is raised to the zero power, apply the zero exponent rule to get \(\left(\frac{p^2 q^3}{r^3}\right)^0 = 1\).
4. Note that the negative sign in front of the parentheses applies to the whole expression, so the expression becomes \(-1\) after simplification.
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

Exponent rules govern how to simplify expressions involving powers, such as multiplying, dividing, and raising powers to powers. Understanding these helps in manipulating expressions before applying the zero exponent rule.

Nonzero Variables Assumption

Assuming variables are nonzero ensures that expressions like (p^2q^3/r^3)^0 are defined, since zero bases raised to zero power are undefined. This assumption allows safe application of exponent rules.