Simplify each expression. Assume all variables represent nonzero real numbers. -(p²q³/r³)⁰

Verified step by step guidance

1. Identify the expression given: \(-\left(\frac{p^{2}q^{3}}{r^{3}}\right)^{0}\).
2. Recall the zero exponent rule: For any nonzero expression \(a\), \(a^{0} = 1\).
3. Apply the zero exponent rule to the expression inside the parentheses: \(\left(\frac{p^{2}q^{3}}{r^{3}}\right)^{0} = 1\).
4. Include the negative sign outside the parentheses: \(-\left(\frac{p^{2}q^{3}}{r^{3}}\right)^{0} = -1\).
5. Conclude that the simplified expression is \(-1\) since all variables are nonzero and the zero exponent rule applies.

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 inside the parentheses.

Properties of Exponents

Exponents indicate repeated multiplication. Understanding how to manipulate powers, such as multiplying, dividing, and raising powers to powers, is essential for simplifying algebraic expressions involving variables with exponents.

Nonzero Variable Assumption

Assuming variables are nonzero ensures that expressions like division by variables or zero exponents are valid. This prevents undefined operations and allows the use of exponent rules safely.